In this paper, an efficient numerical scheme based on uniform Haar wavelets and the quasilinearization process is proposed for the numerical simulation of time dependent nonlinear Burgers’ equation. The equation has great importance in many physical problems such as fluid dynamics, turbulence, sound waves in a viscous medium etc. The Haar wavelet basis permits to enlarge the class of functions ...

REFERENCES: Bellman, R. E. (1967). Introduction to the Mathematical Theory of Control Processes. New York: Academic Press. Bellman, R. E., Jacquez, J., Kalaba, R., & Schwimmer, S. (1976). Quasilinearization and the estimation of chemical rate constants from raw kinetic data. Mathematical Biosciences, 1, 71-76. Ferris, D. P., & Farley, C. T. (1997). Interaction of leg stiffness and surfaces stif...

This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equa...

The paper presents a significant improvement to the implementation of the spectral relaxation method (SRM) for solving nonlinear partial differential equations that arise in the modelling of fluid flow problems. Previously the SRM utilized the spectral method to discretize derivatives in space and finite differences to discretize in time. In this work we seek to improve the performance of the S...