Taylor wavelet analysis and numerical simulation for boundary value problems of higher order under multiple boundary conditions

Abstract

The predominant objective of this study is to simulate higher-order linear and nonlinear initial-boundary value problems using approximation and collocation approach with the bases of Taylor wavelet. Differentiation is utilised in the function approximation approach to acquire expression for higher-order derivatives as well as solution to an unknown function. The mentioned scheme of wavelet approximation for higher-order differential equations is an intriguing scheme that has the potential to produce accurate and efficient results. The flexibility of the wavelet to the local character of differential equations of higher order corresponds well with the complexity caused by various boundary conditions. This study investigates the effectiveness of wavelet-based approach in solving higher-order differential equations under appropriate initial conditions, boundary conditions and Robin boundary conditions. Furthermore, a thorough error analysis is required to assess the dependability of these solutions. Therefore, maximum and minimum absolute errors, \(L_{2}\) errors, relative error and experimental convergence order at various wavelet bases are evaluated to investigate the performance and effectiveness of the mentioned scheme. We have also compared the approximated solutions with other existing solutions to demonstrate the reliability and accuracy of the mentioned scheme.