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- Title
Haar Wavelet Matrices Designation in Numerical Solution of Ordinary Differential Equations.
- Authors
Chang, Phang; Piau, Phang
- Abstract
Wavelet transforms or wavelet analysis is a recently developed mathematical tool for many problems. Wavelets also can be applied in numerical analysis. In this paper, we apply Haar wavelet methods to solve ordinary differential equations with initial or boundary condition known. To avoid the tedious calculations and to promote the study of wavelets to beginners, we proposed a simple way to perform the calculations for the matrix representation. The procedure applied in this paper is taking the Haar Series for the highest order of differential and integrate the series. Four numerical examples are shown which including first, second, higher order differential equations with constant and variable coefficients. The results show that the proposed way are quite reasonable when compare to exact solution.
- Subjects
HAAR system (Mathematics); WAVELETS (Mathematics); HARMONIC analysis (Mathematics); NUMERICAL analysis; DIFFERENTIAL equations; BOUNDARY value problems
- Publication
IAENG International Journal of Applied Mathematics, 2008, Vol 38, Issue 3, p164
- ISSN
1992-9978
- Publication type
Article