A family of third-order parallel splitting methods for parabolic partial differential equations

Abstract

A family of numerical methods, based upon a new rational approximation to the matrix exponential function, is developed for solving parabolic partial differential equations. These methods are L-acceptable, third-order accurate in space and time, and do not require the use of complex arithmetic. In these methods second-order spatial derivatives are approximated by third-order finite-difference approximations.- Parallel algorithms are developed and tested on the one-dimensional heat equation, with constant coefficients, subject to homogeneous boundary conditions and time-dependent boundary conditions. These methods are also extended to two- and three-dimensional heat equations, with constant coefficients, subject to homogeneous boundary conditions.

Keywords:

• Heat equation
• finite differences
• parallel splitting
• third-order numerical methods

C.R. Categories:

• G1.8

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Notes

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