Hermite Interpolation Approach to High-Order Approximation of Heat Equations

Chinedu Nwaigwe and Azubuike Weli
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Chinedu Nwaigwe: Rivers State University, Nigeria
Azubuike Weli: Rivers State University, Nigeria

European Journal of Mathematics and Statistics, 2023, vol. 4, issue 1, 32-37

Abstract: It is usually desirable to approximate the solution of mathemati- cal problems with high-order of accuracy and preferably using com- pact stencils. This work presents an approach for deriving high-order compact discretization of heat equation with source term. The key contribution of this work is the use of Hermite polynomials to reduce second order spatial derivatives to lower order derivatives. This does not involve the use of the given equation, so it is universal. Then, Tay- lor expansion is used to obtain a compact scheme for first derivatives. This leads to a fourth-order approximation in space. Crank-Nicholson scheme is then applied to derive a fully discrete scheme. The result- ing scheme coincides with the fourth-order compact scheme, but our derivation follows a different philosophy which can be adapted for other equations and higher order accuracy. Two numerical experiments are provided to verify the fourth-order accuracy of the approach.

Keywords: Compact schemes; Heat Equation; Hermite interpolation; high-order schemes (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:epw:ejmath:v:4:y:2023:i:1:id:14208

DOI: 10.24018/ejmath.2023.4.1.208

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