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NUMERICAL SIMULATION OF ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS USING 3-SCALE HAAR WAVELETS

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초록

Elliptic partial differential equations (PDEs) arise in the mathematical modelling of many physical phenomena in science and engineering. In this paper, we obtain the numerical solution of Laplace and Poisson equations using two-dimensional 3-scale Haar wavelets. The elliptic PDEs are converted into a system of algebraic equations that involve a fi nite number of variables. The numerical results are compared with the exact solution to prove the accuracy of the Haar wavelet method. The error analysis of the 3-scale Haar wavelet method proves that the solution improves with the increase in the levels of resolution of the wavelet.

Abstract

Elliptic partial differential equations (PDEs) arise in the mathematical modelling of many physical phenomena in science and engineering. In this paper, we obtain the numerical solution of Laplace and Poisson equations using two-dimensional 3-scale Haar wavelets. The elliptic PDEs are converted into a system of algebraic equations that involve a fi nite number of variables. The numerical results are compared with the exact solution to prove the accuracy of the Haar wavelet method. The error analysis of the 3-scale Haar wavelet method proves that the solution improves with the increase in the levels of resolution of the wavelet.

참고문헌 (33)

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