Method of Lines Transpose: High Order L-Stable ${\mathcal O}(N)$ Schemes for Parabolic Equations Using Successive Convolution

DOI10.1137/15M1035094zbMath1339.65199arXiv1508.03105OpenAlexW2962944067MaRDI QIDQ2810566

Hana Cho, David C. Seal, Andrew J. Christlieb, Matthew F. Causley

Publication date: 3 June 2016

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1508.03105

zbMATH Keywords

Rothe's methodADI schemesparabolic PDEsalternating direction implicit methodsimplicit methodsboundary integral methodsmethod of lines transposetransverse method of linesmultiderivativehigher order L-stable

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Reaction-diffusion equations (35K57) Heat equation (35K05) Integral representations, integral operators, integral equations methods in two dimensions (31A10) Fundamental solutions, Green's function methods, etc. for initial value and initial-boundary value problems involving PDEs (65M80)

Related Items (14)

A transversal method of lines for the numerical modeling of vertical infiltration into the vadose zone ⋮ A kernel based high order ``explicit unconditionally stable scheme for time dependent Hamilton-Jacobi equations ⋮ A WENO-based method of lines transpose approach for Vlasov simulations ⋮ Numerical simulation method of lines together with a pseudospectral method for solving space-time partial differential equations with space left- and right-sided fractional derivative ⋮ A kernel-based explicit unconditionally stable scheme for Hamilton-Jacobi equations on nonuniform meshes ⋮ Method of Lines Transpose: Energy Gradient Flows Using Direct Operator Inversion for Phase-Field Models ⋮ A mixed MoL-TMoL for the numerical solution of the 2D Richards' equation in layered soils ⋮ Parallel algorithms for successive convolution ⋮ On the implementation of a finite volumes scheme with monotone transmission conditions for scalar conservation laws on a star-shaped network ⋮ Method of lines transpose: an efficient unconditionally stable solver for wave propagation ⋮ A Kernel Based Unconditionally Stable Scheme for Nonlinear Parabolic Partial Differential Equations ⋮ Implicit multistage two-derivative discontinuous Galerkin schemes for viscous conservation laws ⋮ Kernel based high order ``explicit unconditionally stable scheme for nonlinear degenerate advection-diffusion equations ⋮ A High Order Finite Difference Weighted Essentially NonOscillatory Scheme with a Kernel-Based Constrained Transport Method for Ideal Magnetohydrodynamics

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