A novel scheme for the hyperbolic partial differential equation through Fibonacci wavelets

Abstract

In this study, we generated the operational matrices of integration based on the Fibonacci wavelets through the concept of linear algebra and developed the novel technique known as the Fibonacci wavelet collocation method (FWCM). The proposed approach extracts the numerical solution of linear hyperbolic partial differential equations (HPDEs). This technique is an efficient and emerging numerical algorithm that converts the considered problem into a system of equations of algebraic type. We obtained desired numerical results in solving this system of algebraic equations with the help of the Newton–Raphson technique. We solved the five problems concerning a minimum level of resolution to strengthen our results. The obtained outcome is compared with the exact and other numerical solutions available in the literature through tables and graphs. The tables and graphical representations clarify the accuracy and efficiency of the proposed technique. Convergence analysis for the proposed method is drawn in terms of the theorems.

Keywords

• Hyperbolic partial differential equations
• Collocation method
• Operational matrix of integration
• Fibonacci wavelets
• Newton–Raphson technique
• 35L02