Efficient numerical algorithm for solving the Benjamin-Bona-Mahony partial differential equation using Fibonacci wavelets and advanced computational techniques

In this article, we have presented a novel and unified numerical strategy for addressing the Benjamin-Bona-Mahony (BBM) type partial differential equations with the use of the Fibonacci wavelets and collocation techniques. This technique is based on transforming the given PDEs into an equivalent integral equation via the wavelet basis approximation and collocation techniques to obtain the wavelet coefficients. Convergence analysis in the form of the theorems was also discussed to prove the 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 and outcomes in tabulated form are given to show how the suggested wavelet method provides enhanced accuracy for a wide range of problems. MATLsoftware is used to execute the computational operations.