Non‐polynomials spline methods for solving a fourth‐order parabolic equation | Zendy

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Non‐polynomials spline methods for solving a fourth‐order parabolic equation

Author(s) -

Khan Arshad

Publication year - 2007

Publication title -

pamm

Language(s) - English

Resource type - Journals

ISSN - 1617-7061

DOI - 10.1002/pamm.200701014

Subject(s) - mathematics , discretization , spline (mechanical) , partial differential equation , mathematical analysis , variable coefficient , polynomial , quintic function , perfect spline , partial derivative , variable (mathematics) , homogeneous , parabolic partial differential equation , differential equation , thin plate spline , spline interpolation , physics , combinatorics , nonlinear system , quantum mechanics , thermodynamics , statistics , bilinear interpolation

In this paper a fourth‐order variable coefficient parabolic partial differential equation, that governs the behaviour of a vibrating beam, is solved by using a three level method based on non‐polynomial quintic spline in space and finite difference discretization in time. We also obtain two new high accuracy schemes of O ( k 4 , h 6 ) and O ( k 4 , h 8 ) and two new schemes which are analogues of Jain's formula for the non‐homogeneous case. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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