Open Access

ARTICLE

A Fictitious Time Integration Method for a Quasilinear Elliptic Boundary Value Problem, Defined in an Arbitrary Plane Domain

Chein-Shan Liu¹

1 Department of Civil Engineering, National Taiwan University, Taipei, Taiwan. E-mail: liucs@ntu.edu.tw

Computers, Materials & Continua 2009, 11(1), 15-32. https://doi.org/10.3970/cmc.2009.011.015

Abstract

Motivated by the evolutionary and dissipative properties of parabolic type partial differential equation (PDE), Liu (2008a) has proposed a natural and mathematically equivalent approach by transforming the quasilinear elliptic PDE into a parabolic one. However, the above paper only considered a rectangular domain in the plane, and did not treat the difficulty arisen from the quasilinear PDE defined in an arbitrary plane domain. In this paper we propose a new technique of internal and boundary residuals in a fictitious rectangular domain, which are driving forces for the ordinary differential equations based on the Fictitious Time Integration Method (FTIM). Several numerical examples validate the performance of the FTIM, which can easily handle the nonlinear boundary value problem, defined in an arbitrary plane domain.

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Keywords

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