Improved Elzaki transform method for singular initial value problems in second order ordinary differential equations

Abstract

In this paper, we proposed a numerical method called the improved Elzaki transform method for solving singular initial value problems in second order ordinary differential equations. The method is used in handling a generalization of this kind of problem. For this purpose, an Elzaki linear operator is defined and evaluated using certain Elzaki transforms properties. The method was experimented for linear and nonlinear singular initial value problems, and the resulting numerical evidences show that the method converges to the exact solution usually in the first iteration. The method requires less computational rigor such that computational, round-off and truncation errors are eliminated. Similarly, results obtained by the improved Elzaki transform method converge favourably to same results obtained using the modified ADM. Also, the standard Elzaki transform method was treated for the same examples considered, and the results obtained were compared with the improved Elzaki transform method to verify the claim that the improved Elzaki transform method is far superior. All computations were performed with the aid of the computer application programme Maple 18 software.

Keywords: Elzaki transform method, Ordinary differential equations, Singular initial value problems, Adomian polynomials, Maple 18 software