Wavelet based quasilinearization method for semi-linear parabolic initial boundary value problems

• Finite difference free wavelets based quasilinearization methods developed for SPIBVP.
• Fisher, Huxley and Newell–Whitehead–Segel equations solved very efficiently.
• Comparison study provided for quasilinearization based on Haar and Legendre wavelets.
• Proposed approach performs better than the methods in the recent literature.

In this paper, numerical methods based on quasilinearization and Haar and Legendre wavelets to solve a class of semi linear parabolic initial boundary value problem (SPIBVP) have been presented. The Haar and Legendre wavelet methods have been successfully combined with quasilinearization to solve SPIBVP efficiently. The presented numerical scheme has been illustrated using appropriate examples including Fisher equation and the obtained results show that the proposed numerical scheme is robust and easy to apply.