The MOL solution of time dependent partial differential equations

DOI10.1016/0898-1221(96)00063-6zbMath0853.65095OpenAlexW1995354615MaRDI QIDQ1921245

Y. Psihoyios, Jeff R. Cash

Publication date: 8 December 1996

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0898-1221(96)00063-6

zbMATH Keywords

method of linesparabolic equationsstiffnessbackward differentiation formulaadvection diffusion problems

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (5)

Solving time dependent PDEs via an improved modified extended BDF scheme ⋮ Class 2 + 1 hybrid BDF-like methods for the numerical solutions of ordinary differential equations ⋮ Boosting the accuracy of finite difference schemes via optimal time step selection and non-iterative defect correction ⋮ Solving nonlinear parabolic PDEs via extended hybrid BDF methods ⋮ Hybrid BDF methods for the numerical solutions of ordinary differential equations

Uses Software

• MEBDF
• DASSL
• PDECHEB

Cites Work

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• Split linear multistep methods for the numerical integration of stiff differential systems
• Explicit advanced step-point (EAS) methods and the EAS2 multistep scheme for the solution of non-stiff initial value problems
• An adaptive method of lines with error control for parabolic equations of the reaction-diffusion type
• Developing software for time-dependent problems using the method of lines and differential-algebraic integrators
• The NUMOL solution of time-dependent PDEs using DESI Runge-Kutta formulae
• Avoiding BDF stability barriers in the MOL solution of advection- dominated problems
• The control of order and steplength for backward differentiation methods
• A‐posteriori error estimates for the finite element method
• Algorithm 690: Chebyshev polynomial software for elliptic-parabolic systems of PDEs
• An MEBDF code for stiff initial value problems
• Implicit-Explicit Methods for Time-Dependent Partial Differential Equations
• Balancing Space and Time Errors in the Method of Lines for Parabolic Equations
• A Test for Instability in the Numerical Solution of Ordinary Differential Equations

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