Computer implementation based a fast numerical method under Fibonacci-wavelet technique for the solution of the Benjamin-Bona-Mahony partial differential equation

Abstract

In this article, we have presented a computationally efficient technique based on the method of  Fibonacci wavelets and collocation technique for the solution of linear and nonlinear Benjamin-Bona-Mahony (BBM) type partial differential equations. These problems are transformed into a system of algebraic equations using truncated Fibonacci wavelet expansions and then simplified using a suitable method. The suggested Fibonacci wavelet approach is worked out for the convergence analysis it is demonstrated that the estimation of a function using Fibonacci wavelets converges uniformly to itself. It is anticipated that the proposed approach would be more efficient and suitable for solving a variety of nonlinear partial differential equations that occur in science and engineering. Examples are given to show how the suggested wavelet method provides enhanced accuracy for a wide range of problems.