Efficient Explicit Improved Scheme for Numerical Solution of Cauchy Problems

Abstract

This study work is focus on to design explicit splendid converging method to estimate numerical result of initial-value-problems (IVP’s) for differential equation in nature ordinary. The stability criteria of the improved scheme are investigated, and corresponding stability region is depicted. Error analysis carried out also affirms accuracy having third order. Error (LTE) is derived by utilizing Taylor’s series expansion to skip higher order term after matching corresponding coefficients. Adding a partial derivative inside function evaluation raises convergence and reduces both errors (maximum and last). Based on results for improved scheme to illustrate the accuracy and efficiency. The comparisons of the improved and existing schemes having same order of local accuracy are discussed. Looking at numerical results, the improved scheme gives the better result in the comparison of existing few same order method. Stability is proved to examine behavior of method and its region is visualized. Consistency is investigated that is showing how error shrink to zero. the numerical result is validated and illustrated graphically via utilizing MATLAB 2023a software.