Parallel Algorithms for Fourth-Order Parabolic Equations

Arigu, M. A.; Twizell, E. H.; Gumel, Abba B.

doi:10.1080/10637199508915515

Cited by 1 publication

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“…Methods of higher order than second in time have been developed by using the method of lines with finite differences for the spatial discretization and higher order methods for the solution of the resulting IVP for a system of second order ordinary differential equations; see [89,166,167], and [16] where equation (1.9) is considered. Khaliq and Twizell [90] generalized this approach to formulate a family of FDMs for equation (1.15) in which a = a(x).…”

Section: One Dimensional Problemsmentioning

confidence: 99%

Numerical Methods for Schrödinger-Type Problems

Fairweather¹,

Khebchareon²

2002

Applied Optimization

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Several physical phenomena are modeled by initial-boundary value problems which can be formulated as SchrOdinger -type systems of partial differential equations. In this paper, two classes of problems of this kind, Schrodinger equations, which arise in various areas of physics, and certain vibration problems from civil and mechanical engineering, are considered. A survey of numerical methods for solving linear and nonlinear problems in one and several space variables is presented, with special attention being devoted to the parabolic wave equation, the cubic Schrodinger equation, and to fourth order parabolic equations arising in vibrating beam and plate problems. Recently developed finite element methods for solving SchrOdinger-type systems are also outlined.Keywords: Schrodinger systems, linear and nonlinear Schrodinger equations, parabolic wave equation, vibrating beams and plates, fourth order parabolic equations, finite difference methods, finite element Galerkin methods, orthogonal spline collocation methods, spectral methods IntroductionWe consider the numerical solution of problems that can be written as initialboundary value problems (IBVPs) for real systems of partial differential equations of the form

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