A study on different classes of differential equations by semi-analytical and numerical techniques

Abstract This study uses the Homotopy analysis method (HAM) and Haar wavelet transform (HWT) to give an innovative technique for approximating to the nonlinear ordinary differential equations (ODEs), a system of ODEs, and partial differential equations (PDEs). HAM is a potent semi-analytical method that works well with linear and nonlinear problems studied. HWT is a numerical technique that effectively discretizes differential equations (DEs) simultaneously. A robust analytical method builds a family of equations that smoothly transforms the original nonlinear equation into a straightforward linear issue using the topological concept of homotopy. This allows the derivation of extremely precise series solutions. Real-world application problems are solved to analyze the correctness and effectiveness of the projected system.