Alternating direction implicit orthogonal spline collocation on some non-rectangular regions with inconsistent partitions

DOI10.1007/S11075-016-0187-7zbMath1362.65111OpenAlexW2491742562MaRDI QIDQ521924

Ryan I. Fernandes, Bernard Bialecki

Publication date: 12 April 2017

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-016-0187-7

zbMATH Keywords

parabolic equationinitial boundary value problemalternating direction implicit methodparabolic problemnumerical resulttwo point boundary value problemCrank Nicolsonnon-rectangular regionorthogonal spline collocation

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Linear boundary value problems for ordinary differential equations (34B05)

Related Items (4)

High-order orthogonal spline collocation method with graded meshes for two-dimensional fractional evolution integro-differential equation ⋮ Unnamed Item ⋮ A fast ADI orthogonal spline collocation method with graded meshes for the two-dimensional fractional integro-differential equation ⋮ BDF ADI orthogonal spline collocation scheme for the fractional integro-differential equation with two weakly singular kernels

Uses Software

• COLROW
• ARCELO

Cites Work

• Unnamed Item
• Unnamed Item
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• Improved forms of the alternating direction methods of Douglas, Peaceman, and Rachford for solving parabolic and elliptic equations
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• The Numerical Solution of Parabolic and Elliptic Differential Equations
• An Alternating-Direction Implicit Orthogonal Spline Collocation Scheme for Nonlinear Parabolic Problems on Rectangular Polygons
• A high-order ADI method for parabolic problems with variable coefficients
• FORTRAN Packages for Solving Certain Almost Block Diagonal Linear Systems by Modified Alternate Row and Column Elimination
• An Orthogonal Spline Collocation Alternating Direction Implicit Crank--Nicolson Method for Linear Parabolic Problems on Rectangles
• The Direct Solution of the Discrete Poisson Equation on Irregular Regions
• A New Computational Procedure for A.D.I. Methods
• High-Order ADI Schemes for Convection-Diffusion Equations with Mixed Derivative Terms

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