Hermite wavelets method for the numerical solution of linear and nonlinear singular initial and boundary value problems

In this article, Modified Hermite wavelets based numerical method is developed for the solution of singular initial and boundary value problems. It consists of reducing the differential equations with the associated initial and boundary conditions into system of algebraic equations by expanding the unknown function as a series of Hermite wavelets with unknown coefficients. Obtained system of equations are solved using Newton’s iterative method through Matlab. Illustrative examples are considered to demonstrate the applicability and accuracy of the proposed technique. Obtained results are compared favorably with the exact solutions. Also, we proved the theorem reveals that, when exact solution can be obtained by the proposed method and theorems regarding convergence and error analysis.