Wavelet based Solution to Some Time Dependent Two-Point Initial Boundary Value Problems with Non-Linear (Convective) Non-Periodic Boundary Conditions

R.K. Nekkanti and H.N. Narang (USA)


Wavelets, Galerkin method, Convective boundary conditions, Non-periodic boundary conditions, Boundary Value Problems, Backward Implicit Differencing Technique.


The Wavelet solution for boundary-value problems is relatively new and has been mainly restricted to the solutions in data compression, image processing and recently to the solution of differential equations with periodic boundary conditions. This paper is concerned with the wavelet-based Galerkin's solution to a time dependent two-point initial-boundary-value problem with non-linear non-periodic boundary conditions. The wavelet method can offer several advantages in solving the initial boundary-value problems than the traditional methods such as Fourier series, Finite Differences and Finite Elements by reducing the computational time near singularities because of its multi-resolution character. In order to demonstrate the wavelet technique to initial boundary value problems with non-linear non-periodic boundary conditions, we extend our prior research of solution technique to parabolic equations of one dimensional differential equation of heat conduction with non-linear (convective) boundary conditions. The results of the wavelet solutions are examined and they are found to comply with the expected results. This paper on the whole indicates that the wavelet technique is a strong contender for solving two-point boundary value problems with non-linear non-periodic boundary conditions.

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