A Survey of Higher-order Methods for the Numerical Integration of Semidiscrete Parabolic Problems

DOI10.1093/imanum/4.4.375zbMath0561.65087OpenAlexW2077424134MaRDI QIDQ5186688

W. L. Seward, R. L. Johnston, Graeme Fairweather

Publication date: 1984

Published in: IMA Journal of Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1093/imanum/4.4.375

zbMATH Keywords

surveystabilitysystemsfinite-differenceextrapolationfinite-elementcomputational efficiencyhigher-order methodsRunge-Kutta formulaemultistep formulaesemidiscrete parabolic problems

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Method of lines for boundary value problems involving PDEs (65N40) Computer aspects of numerical algorithms (65Yxx)

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The numerical solution of large systems of stiff IVPs for ODEs ⋮ A low-order meshless model for multidimensional heat conduction problems ⋮ A fourth order alternating direction method based on the (2, 2) - Padé Approximant ⋮ Towards a general integration algorithm for time-dependent one- dimensional systems of parabolic partial differential equations using the method of lines ⋮ A NEW TIME-STEPPING SCHEME FOR THE NETWORK MODELLING OF DIFFUSION ⋮ A composite integration scheme for the numerical solution of systems of parabolic PDEs in one space dimension ⋮ Stiff ODE solvers: A review of current and coming attractions ⋮ Time-continuous Galerkin methods for linear heat conduction problems ⋮ The Nørsett time integration methodology for finite element transient analysis

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