Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands · 1996 · 47 citations · 0 references
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ComputingMathematicsAlgorithmsComputational MechanicsComputational PhysicsAdaptive Mesh RefinementConvergence AnalysisFinite Difference MethodsNumerical AlgorithmsNumerical AnalysisNumerical Methods For Differential EquationsFinite Difference ApproximationFinite Difference SchemesNonlinear EvolutionNumerical ContinuationSolution ContinuationStationary Solutions
A numerical algorithm for continuation of stationary solutions to nonlinear evolution problems representable in the form $$ begin{array{ll u_t=F(u_{xx,u_{x,u,x,alpha),& 0 < x < 1, f^{0(u_x,u,alpha)=0,& x=0, f^{1(u_x,u,alpha)=0,& x=1, end{array $$ is described as implemented in {sc content. Here $F:{Bbb R^n times {Bbb R^n times {Bbb R^n times {Bbb R^m to {Bbb R^n$ and $f^{0,1:{Bbb R^n times {Bbb R^n times {Bbb R^m to {Bbb R^n$ are sufficiently smooth nonlinear functions. The algorithm is based on the second-order finite-difference approximation with an adaptive non-uniform mesh selection. Special methods for efficient solution of linear systems appearing in the continuation are presented. Several examples are given.