From: Wolfgang Bangerth Date: Wed, 24 May 2023 17:04:23 +0000 (-0600) Subject: Add tests for recoverable and irrecoverable situations. X-Git-Tag: v9.5.0-rc1~188^2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=refs%2Fpull%2F15263%2Fhead;p=dealii.git Add tests for recoverable and irrecoverable situations. --- diff --git a/tests/sundials/ida_04.cc b/tests/sundials/ida_04.cc new file mode 100644 index 0000000000..8f9111783f --- /dev/null +++ b/tests/sundials/ida_04.cc @@ -0,0 +1,164 @@ +//----------------------------------------------------------- +// +// Copyright (C) 2017 - 2022 by the deal.II authors +// +// This file is part of the deal.II library. +// +// The deal.II library is free software; you can use it, redistribute +// it, and/or modify it under the terms of the GNU Lesser General +// Public License as published by the Free Software Foundation; either +// version 2.1 of the License, or (at your option) any later version. +// The full text of the license can be found in the file LICENSE.md at +// the top level directory of deal.II. +// +//----------------------------------------------------------- + +#include + +#include +#include + +#include + +#include "../tests.h" + + +/** + * Like the _03 test, but throw an irrecoverable exception if the time + * step is longer than 0.1. + * + * Solve the exponential decay problem: + * + * y' = -k y + * y (0) = 1 + * + * with k=2. That is + * + * F(y', y, t) = y' + k y = 0 + * y_0 = 1 + * + * The exact solution is + * + * y(t) = exp(-k*t) + * + * The Jacobian we then need to assemble is the following: + * + * J = dF/dy + alpha dF/dy' + * = k + alpha 1 + * = (k+alpha) + */ +class HarmonicOscillator +{ +public: + HarmonicOscillator( + double _kappa, + const typename SUNDIALS::IDA>::AdditionalData &data) + : time_stepper(data) + , y(1) + , y_dot(1) + , kappa(_kappa) + , last_residual_eval_time(0) + { + using VectorType = Vector; + + time_stepper.reinit_vector = [&](VectorType &v) { v.reinit(1); }; + + + time_stepper.residual = [&](const double t, + const VectorType &y, + const VectorType &y_dot, + VectorType & res) { + deallog << "Evaluating residual at t=" << t << std::endl; + + if (t > last_residual_eval_time + 0.1) + { + deallog << "Time step is too large: " << t - last_residual_eval_time + << ". Failing irrecoverably." << std::endl; + + throw ExcMessage("Irrecoverable exception."); + } + + res[0] = y_dot[0] + kappa * y[0]; + last_residual_eval_time = t; + }; + + time_stepper.setup_jacobian = [&](const double, + const VectorType &, + const VectorType &, + const double alpha) { + J = kappa + alpha; + }; + + // Used only in ver < 4.0.0 + time_stepper.solve_jacobian_system = + [&](const VectorType &src, VectorType &dst) { dst[0] = src[0] / J; }; + + // Used in ver >= 4.0.0 + time_stepper.solve_with_jacobian = + [&](const VectorType &src, VectorType &dst, const double) { + dst[0] = src[0] / J; + }; + + time_stepper.output_step = [&](const double t, + const VectorType & sol, + const VectorType & sol_dot, + const unsigned int step_number) { + deallog << "Intermediate output:" << std::endl; + deallog << " t =" << t << std::endl; + deallog << " y =" << sol[0] << " (exact: " << std::exp(-kappa * t) + << ')' << std::endl; + deallog << " y'=" << sol_dot[0] + << " (exact: " << -kappa * std::exp(-kappa * t) << ')' + << std::endl; + }; + } + + void + run() + { + y[0] = 1; + y_dot[0] = -kappa; + try + { + time_stepper.solve_dae(y, y_dot); + } + catch (const std::exception &exc) + { + deallog << "Caught an irrecoverable exception in a callback:" + << std::endl + << exc.what() << std::endl; + } + } + + SUNDIALS::IDA> time_stepper; + +private: + Vector y; + Vector y_dot; + double J; + double kappa; + double last_residual_eval_time; +}; + + +int +main() +{ + initlog(); + deallog << std::setprecision(10); + + SUNDIALS::IDA>::AdditionalData data; + ParameterHandler prm; + data.add_parameters(prm); + + // std::ofstream ofile(SOURCE_DIR "/ida_04.prm"); + // prm.print_parameters(ofile, ParameterHandler::ShortText); + // ofile.close(); + + std::ifstream ifile(SOURCE_DIR "/ida_04_in.prm"); + prm.parse_input(ifile); + + + HarmonicOscillator ode(2.0, data); + ode.run(); +} diff --git a/tests/sundials/ida_04.output b/tests/sundials/ida_04.output new file mode 100644 index 0000000000..41b39a7947 --- /dev/null +++ b/tests/sundials/ida_04.output @@ -0,0 +1,18 @@ + +DEAL::Intermediate output: +DEAL:: t =0.000000000 +DEAL:: y =1.000000000 (exact: 1.000000000) +DEAL:: y'=-2.000000000 (exact: -2.000000000) +DEAL::Evaluating residual at t=0.2000000000 +DEAL::Time step is too large: 0.2000000000. Failing irrecoverably. +DEAL::Caught an irrecoverable exception in a callback: +DEAL:: +-------------------------------------------------------- +An error occurred in line <0> of file <> in function + +The violated condition was: + +Additional information: + Irrecoverable exception. +-------------------------------------------------------- + diff --git a/tests/sundials/ida_04_in.prm b/tests/sundials/ida_04_in.prm new file mode 100644 index 0000000000..957081de90 --- /dev/null +++ b/tests/sundials/ida_04_in.prm @@ -0,0 +1,19 @@ +set Final time = 2 +set Initial time = 0 +set Time interval between each output = 0.2 +subsection Error control + set Absolute error tolerance = 1e-10 + set Ignore algebraic terms for error computations = true + set Relative error tolerance = 1e-10 +end +subsection Initial condition correction parameters + set Correction type at initial time = none + set Correction type after restart = none + set Maximum number of nonlinear iterations = 10 +end +subsection Running parameters + set Initial step size = 0.2 # start with a large time step + set Maximum number of nonlinear iterations = 10 + set Maximum order of BDF = 5 + set Minimum step size = 1e-7 +end diff --git a/tests/sundials/ida_05.cc b/tests/sundials/ida_05.cc new file mode 100644 index 0000000000..06ea411af1 --- /dev/null +++ b/tests/sundials/ida_05.cc @@ -0,0 +1,165 @@ +//----------------------------------------------------------- +// +// Copyright (C) 2017 - 2022 by the deal.II authors +// +// This file is part of the deal.II library. +// +// The deal.II library is free software; you can use it, redistribute +// it, and/or modify it under the terms of the GNU Lesser General +// Public License as published by the Free Software Foundation; either +// version 2.1 of the License, or (at your option) any later version. +// The full text of the license can be found in the file LICENSE.md at +// the top level directory of deal.II. +// +//----------------------------------------------------------- + +#include + +#include +#include + +#include + +#include "../tests.h" + + +/** + * Like the _03 test, but throw a recoverable exception if the time + * step is longer than 0.1. We will hopefully see that the solver + * reduces the time step and tries again. + * + * Solve the exponential decay problem: + * + * y' = -k y + * y (0) = 1 + * + * with k=2. That is + * + * F(y', y, t) = y' + k y = 0 + * y_0 = 1 + * + * The exact solution is + * + * y(t) = exp(-k*t) + * + * The Jacobian we then need to assemble is the following: + * + * J = dF/dy + alpha dF/dy' + * = k + alpha 1 + * = (k+alpha) + */ +class HarmonicOscillator +{ +public: + HarmonicOscillator( + double _kappa, + const typename SUNDIALS::IDA>::AdditionalData &data) + : time_stepper(data) + , y(1) + , y_dot(1) + , kappa(_kappa) + , last_residual_eval_time(0) + { + using VectorType = Vector; + + time_stepper.reinit_vector = [&](VectorType &v) { v.reinit(1); }; + + + time_stepper.residual = [&](const double t, + const VectorType &y, + const VectorType &y_dot, + VectorType & res) { + deallog << "Evaluating residual at t=" << t << std::endl; + + if (t > last_residual_eval_time + 0.1) + { + deallog << "Time step is too large: " << t - last_residual_eval_time + << ". Failing recoverably." << std::endl; + + throw RecoverableUserCallbackError(); + } + + res[0] = y_dot[0] + kappa * y[0]; + last_residual_eval_time = t; + }; + + time_stepper.setup_jacobian = [&](const double, + const VectorType &, + const VectorType &, + const double alpha) { + J = kappa + alpha; + }; + + // Used only in ver < 4.0.0 + time_stepper.solve_jacobian_system = + [&](const VectorType &src, VectorType &dst) { dst[0] = src[0] / J; }; + + // Used in ver >= 4.0.0 + time_stepper.solve_with_jacobian = + [&](const VectorType &src, VectorType &dst, const double) { + dst[0] = src[0] / J; + }; + + time_stepper.output_step = [&](const double t, + const VectorType & sol, + const VectorType & sol_dot, + const unsigned int step_number) { + deallog << "Intermediate output:" << std::endl; + deallog << " t =" << t << std::endl; + deallog << " y =" << sol[0] << " (exact: " << std::exp(-kappa * t) + << ')' << std::endl; + deallog << " y'=" << sol_dot[0] + << " (exact: " << -kappa * std::exp(-kappa * t) << ')' + << std::endl; + }; + } + + void + run() + { + y[0] = 1; + y_dot[0] = -kappa; + try + { + time_stepper.solve_dae(y, y_dot); + } + catch (const std::exception &exc) + { + deallog << "Caught an irrecoverable exception in a callback:" + << std::endl + << exc.what() << std::endl; + } + } + + SUNDIALS::IDA> time_stepper; + +private: + Vector y; + Vector y_dot; + double J; + double kappa; + double last_residual_eval_time; +}; + + +int +main() +{ + initlog(); + deallog << std::setprecision(10); + + SUNDIALS::IDA>::AdditionalData data; + ParameterHandler prm; + data.add_parameters(prm); + + // std::ofstream ofile(SOURCE_DIR "/ida_04.prm"); + // prm.print_parameters(ofile, ParameterHandler::ShortText); + // ofile.close(); + + std::ifstream ifile(SOURCE_DIR "/ida_04_in.prm"); + prm.parse_input(ifile); + + + HarmonicOscillator ode(2.0, data); + ode.run(); +} diff --git a/tests/sundials/ida_05.output b/tests/sundials/ida_05.output new file mode 100644 index 0000000000..2422eb30ce --- /dev/null +++ b/tests/sundials/ida_05.output @@ -0,0 +1,282 @@ + +DEAL::Intermediate output: +DEAL:: t =0.000000000 +DEAL:: y =1.000000000 (exact: 1.000000000) +DEAL:: y'=-2.000000000 (exact: -2.000000000) +DEAL::Evaluating residual at t=0.2000000000 +DEAL::Time step is too large: 0.2000000000. Failing recoverably. +DEAL::Evaluating residual at t=0.05000000000 +DEAL::Evaluating residual at t=0.05000000000 +DEAL::Evaluating residual at t=0.01250000000 +DEAL::Evaluating residual at t=0.01250000000 +DEAL::Evaluating residual at t=0.003125000000 +DEAL::Evaluating residual at t=0.003125000000 +DEAL::Evaluating residual at t=0.0007812500000 +DEAL::Evaluating residual at t=0.0007812500000 +DEAL::Evaluating residual at t=0.0001953125000 +DEAL::Evaluating residual at t=0.0001953125000 +DEAL::Evaluating residual at t=4.882812500e-05 +DEAL::Evaluating residual at t=4.882812500e-05 +DEAL::Evaluating residual at t=1.220703125e-05 +DEAL::Evaluating residual at t=1.220703125e-05 +DEAL::Evaluating residual at t=3.051757813e-06 +DEAL::Evaluating residual at t=3.051757813e-06 +DEAL::Evaluating residual at t=9.155273438e-06 +DEAL::Evaluating residual at t=9.155273438e-06 +DEAL::Evaluating residual at t=1.525878906e-05 +DEAL::Evaluating residual at t=2.136230469e-05 +DEAL::Evaluating residual at t=3.356933594e-05 +DEAL::Evaluating residual at t=3.356933594e-05 +DEAL::Evaluating residual at t=4.577636719e-05 +DEAL::Evaluating residual at t=5.798339844e-05 +DEAL::Evaluating residual at t=7.019042969e-05 +DEAL::Evaluating residual at t=9.460449219e-05 +DEAL::Evaluating residual at t=0.0001434326172 +DEAL::Evaluating residual at t=0.0001434326172 +DEAL::Evaluating residual at t=0.0002410888672 +DEAL::Evaluating residual at t=0.0002410888672 +DEAL::Evaluating residual at t=0.0004364013672 +DEAL::Evaluating residual at t=0.0004364013672 +DEAL::Evaluating residual at t=0.0006317138672 +DEAL::Evaluating residual at t=0.0008270263672 +DEAL::Evaluating residual at t=0.001022338867 +DEAL::Evaluating residual at t=0.001412963867 +DEAL::Evaluating residual at t=0.001412963867 +DEAL::Evaluating residual at t=0.001803588867 +DEAL::Evaluating residual at t=0.002194213867 +DEAL::Evaluating residual at t=0.002975463867 +DEAL::Evaluating residual at t=0.002975463867 +DEAL::Evaluating residual at t=0.003756713867 +DEAL::Evaluating residual at t=0.004537963867 +DEAL::Evaluating residual at t=0.005319213867 +DEAL::Evaluating residual at t=0.006881713867 +DEAL::Evaluating residual at t=0.006881713867 +DEAL::Evaluating residual at t=0.008444213867 +DEAL::Evaluating residual at t=0.01000671387 +DEAL::Evaluating residual at t=0.01156921387 +DEAL::Evaluating residual at t=0.01313171387 +DEAL::Evaluating residual at t=0.01625671387 +DEAL::Evaluating residual at t=0.01625671387 +DEAL::Evaluating residual at t=0.01938171387 +DEAL::Evaluating residual at t=0.02250671387 +DEAL::Evaluating residual at t=0.02563171387 +DEAL::Evaluating residual at t=0.02875671387 +DEAL::Evaluating residual at t=0.03500671387 +DEAL::Evaluating residual at t=0.03500671387 +DEAL::Evaluating residual at t=0.04125671387 +DEAL::Evaluating residual at t=0.04750671387 +DEAL::Evaluating residual at t=0.05375671387 +DEAL::Evaluating residual at t=0.06000671387 +DEAL::Evaluating residual at t=0.06625671387 +DEAL::Evaluating residual at t=0.07250671387 +DEAL::Evaluating residual at t=0.07250671387 +DEAL::Evaluating residual at t=0.07875671387 +DEAL::Evaluating residual at t=0.08500671387 +DEAL::Evaluating residual at t=0.09125671387 +DEAL::Evaluating residual at t=0.09750671387 +DEAL::Evaluating residual at t=0.1100067139 +DEAL::Evaluating residual at t=0.1100067139 +DEAL::Evaluating residual at t=0.1212567139 +DEAL::Evaluating residual at t=0.1212567139 +DEAL::Evaluating residual at t=0.1325067139 +DEAL::Evaluating residual at t=0.1437567139 +DEAL::Evaluating residual at t=0.1550067139 +DEAL::Evaluating residual at t=0.1662567139 +DEAL::Evaluating residual at t=0.1775067139 +DEAL::Evaluating residual at t=0.1887567139 +DEAL::Evaluating residual at t=0.2000067139 +DEAL::Intermediate output: +DEAL:: t =0.2000000000 +DEAL:: y =0.6703200462 (exact: 0.6703200460) +DEAL:: y'=-1.340640091 (exact: -1.340640092) +DEAL::Evaluating residual at t=0.2112567139 +DEAL::Evaluating residual at t=0.2225067139 +DEAL::Evaluating residual at t=0.2337567139 +DEAL::Evaluating residual at t=0.2450067139 +DEAL::Evaluating residual at t=0.2562567139 +DEAL::Evaluating residual at t=0.2675067139 +DEAL::Evaluating residual at t=0.2787567139 +DEAL::Evaluating residual at t=0.2900067139 +DEAL::Evaluating residual at t=0.3012567139 +DEAL::Evaluating residual at t=0.3125067139 +DEAL::Evaluating residual at t=0.3237567139 +DEAL::Evaluating residual at t=0.3350067139 +DEAL::Evaluating residual at t=0.3462567139 +DEAL::Evaluating residual at t=0.3575067139 +DEAL::Evaluating residual at t=0.3687567139 +DEAL::Evaluating residual at t=0.3800067139 +DEAL::Evaluating residual at t=0.3912567139 +DEAL::Evaluating residual at t=0.4025067139 +DEAL::Intermediate output: +DEAL:: t =0.4000000000 +DEAL:: y =0.4493289645 (exact: 0.4493289641) +DEAL:: y'=-0.8986579278 (exact: -0.8986579282) +DEAL::Evaluating residual at t=0.4137567139 +DEAL::Evaluating residual at t=0.4250067139 +DEAL::Evaluating residual at t=0.4362567139 +DEAL::Evaluating residual at t=0.4475067139 +DEAL::Evaluating residual at t=0.4587567139 +DEAL::Evaluating residual at t=0.4700067139 +DEAL::Evaluating residual at t=0.4812567139 +DEAL::Evaluating residual at t=0.4925067139 +DEAL::Evaluating residual at t=0.5037567139 +DEAL::Evaluating residual at t=0.5150067139 +DEAL::Evaluating residual at t=0.5262567139 +DEAL::Evaluating residual at t=0.5375067139 +DEAL::Evaluating residual at t=0.5487567139 +DEAL::Evaluating residual at t=0.5600067139 +DEAL::Evaluating residual at t=0.5712567139 +DEAL::Evaluating residual at t=0.5825067139 +DEAL::Evaluating residual at t=0.5937567139 +DEAL::Evaluating residual at t=0.6050067139 +DEAL::Intermediate output: +DEAL:: t =0.6000000000 +DEAL:: y =0.3011942124 (exact: 0.3011942119) +DEAL:: y'=-0.6023884237 (exact: -0.6023884238) +DEAL::Evaluating residual at t=0.6162567139 +DEAL::Evaluating residual at t=0.6275067139 +DEAL::Evaluating residual at t=0.6387567139 +DEAL::Evaluating residual at t=0.6500067139 +DEAL::Evaluating residual at t=0.6612567139 +DEAL::Evaluating residual at t=0.6725067139 +DEAL::Evaluating residual at t=0.6837567139 +DEAL::Evaluating residual at t=0.6950067139 +DEAL::Evaluating residual at t=0.7062567139 +DEAL::Evaluating residual at t=0.7175067139 +DEAL::Evaluating residual at t=0.7287567139 +DEAL::Evaluating residual at t=0.7400067139 +DEAL::Evaluating residual at t=0.7512567139 +DEAL::Evaluating residual at t=0.7625067139 +DEAL::Evaluating residual at t=0.7737567139 +DEAL::Evaluating residual at t=0.7850067139 +DEAL::Evaluating residual at t=0.7962567139 +DEAL::Evaluating residual at t=0.8075067139 +DEAL::Intermediate output: +DEAL:: t =0.8000000000 +DEAL:: y =0.2018965185 (exact: 0.2018965180) +DEAL:: y'=-0.4037930361 (exact: -0.4037930360) +DEAL::Evaluating residual at t=0.8187567139 +DEAL::Evaluating residual at t=0.8300067139 +DEAL::Evaluating residual at t=0.8412567139 +DEAL::Evaluating residual at t=0.8525067139 +DEAL::Evaluating residual at t=0.8637567139 +DEAL::Evaluating residual at t=0.8750067139 +DEAL::Evaluating residual at t=0.8862567139 +DEAL::Evaluating residual at t=0.8975067139 +DEAL::Evaluating residual at t=0.9087567139 +DEAL::Evaluating residual at t=0.9200067139 +DEAL::Evaluating residual at t=0.9312567139 +DEAL::Evaluating residual at t=0.9425067139 +DEAL::Evaluating residual at t=0.9537567139 +DEAL::Evaluating residual at t=0.9650067139 +DEAL::Evaluating residual at t=0.9762567139 +DEAL::Evaluating residual at t=0.9875067139 +DEAL::Evaluating residual at t=0.9987567139 +DEAL::Evaluating residual at t=1.010006714 +DEAL::Intermediate output: +DEAL:: t =1.000000000 +DEAL:: y =0.1353352836 (exact: 0.1353352832) +DEAL:: y'=-0.2706705668 (exact: -0.2706705665) +DEAL::Evaluating residual at t=1.021256714 +DEAL::Evaluating residual at t=1.032506714 +DEAL::Evaluating residual at t=1.043756714 +DEAL::Evaluating residual at t=1.055006714 +DEAL::Evaluating residual at t=1.066256714 +DEAL::Evaluating residual at t=1.077506714 +DEAL::Evaluating residual at t=1.088756714 +DEAL::Evaluating residual at t=1.100006714 +DEAL::Evaluating residual at t=1.111256714 +DEAL::Evaluating residual at t=1.122506714 +DEAL::Evaluating residual at t=1.133756714 +DEAL::Evaluating residual at t=1.145006714 +DEAL::Evaluating residual at t=1.156256714 +DEAL::Evaluating residual at t=1.167506714 +DEAL::Evaluating residual at t=1.178756714 +DEAL::Evaluating residual at t=1.190006714 +DEAL::Evaluating residual at t=1.201256714 +DEAL::Intermediate output: +DEAL:: t =1.200000000 +DEAL:: y =0.09071795362 (exact: 0.09071795329) +DEAL:: y'=-0.1814359070 (exact: -0.1814359066) +DEAL::Evaluating residual at t=1.212506714 +DEAL::Evaluating residual at t=1.223756714 +DEAL::Evaluating residual at t=1.235006714 +DEAL::Evaluating residual at t=1.246256714 +DEAL::Evaluating residual at t=1.257506714 +DEAL::Evaluating residual at t=1.268756714 +DEAL::Evaluating residual at t=1.280006714 +DEAL::Evaluating residual at t=1.291256714 +DEAL::Evaluating residual at t=1.302506714 +DEAL::Evaluating residual at t=1.313756714 +DEAL::Evaluating residual at t=1.325006714 +DEAL::Evaluating residual at t=1.336256714 +DEAL::Evaluating residual at t=1.347506714 +DEAL::Evaluating residual at t=1.358756714 +DEAL::Evaluating residual at t=1.370006714 +DEAL::Evaluating residual at t=1.381256714 +DEAL::Evaluating residual at t=1.392506714 +DEAL::Evaluating residual at t=1.403756714 +DEAL::Intermediate output: +DEAL:: t =1.400000000 +DEAL:: y =0.06081006289 (exact: 0.06081006263) +DEAL:: y'=-0.1216201256 (exact: -0.1216201253) +DEAL::Evaluating residual at t=1.415006714 +DEAL::Evaluating residual at t=1.426256714 +DEAL::Evaluating residual at t=1.437506714 +DEAL::Evaluating residual at t=1.448756714 +DEAL::Evaluating residual at t=1.460006714 +DEAL::Evaluating residual at t=1.471256714 +DEAL::Evaluating residual at t=1.482506714 +DEAL::Evaluating residual at t=1.493756714 +DEAL::Evaluating residual at t=1.505006714 +DEAL::Evaluating residual at t=1.516256714 +DEAL::Evaluating residual at t=1.527506714 +DEAL::Evaluating residual at t=1.538756714 +DEAL::Evaluating residual at t=1.550006714 +DEAL::Evaluating residual at t=1.561256714 +DEAL::Evaluating residual at t=1.572506714 +DEAL::Evaluating residual at t=1.583756714 +DEAL::Evaluating residual at t=1.595006714 +DEAL::Evaluating residual at t=1.606256714 +DEAL::Intermediate output: +DEAL:: t =1.600000000 +DEAL:: y =0.04076220418 (exact: 0.04076220398) +DEAL:: y'=-0.08152440821 (exact: -0.08152440796) +DEAL::Evaluating residual at t=1.617506714 +DEAL::Evaluating residual at t=1.628756714 +DEAL::Evaluating residual at t=1.640006714 +DEAL::Evaluating residual at t=1.651256714 +DEAL::Evaluating residual at t=1.662506714 +DEAL::Evaluating residual at t=1.673756714 +DEAL::Evaluating residual at t=1.685006714 +DEAL::Evaluating residual at t=1.707506714 +DEAL::Evaluating residual at t=1.707506714 +DEAL::Evaluating residual at t=1.727756714 +DEAL::Evaluating residual at t=1.727756714 +DEAL::Evaluating residual at t=1.748006714 +DEAL::Evaluating residual at t=1.768256714 +DEAL::Evaluating residual at t=1.788506714 +DEAL::Evaluating residual at t=1.808756714 +DEAL::Intermediate output: +DEAL:: t =1.800000000 +DEAL:: y =0.02732372275 (exact: 0.02732372245) +DEAL:: y'=-0.05464744359 (exact: -0.05464744489) +DEAL::Evaluating residual at t=1.829006714 +DEAL::Evaluating residual at t=1.849256714 +DEAL::Evaluating residual at t=1.869506714 +DEAL::Evaluating residual at t=1.889756714 +DEAL::Evaluating residual at t=1.910006714 +DEAL::Evaluating residual at t=1.930256714 +DEAL::Evaluating residual at t=1.950506714 +DEAL::Evaluating residual at t=1.970756714 +DEAL::Evaluating residual at t=1.991006714 +DEAL::Evaluating residual at t=2.000000000 +DEAL::Evaluating residual at t=2.000000000 +DEAL::Intermediate output: +DEAL:: t =2.000000000 +DEAL:: y =0.01831563933 (exact: 0.01831563889) +DEAL:: y'=-0.03663127916 (exact: -0.03663127778) +DEAL::Intermediate output: +DEAL:: t =2.000000000 +DEAL:: y =0.01831563933 (exact: 0.01831563889) +DEAL:: y'=-0.03663127916 (exact: -0.03663127778)