Theoretical and Numerical Discussion for the Mixed Integro–Differential Equations

Abstract

In this paper, we tend to apply the proposed modified Laplace Adomian decomposition method that is the coupling of Laplace transform and Adomian decomposition method. The modified Laplace Adomian decomposition method is applied to solve the Fredholm–Volterra integro–differential equations of the second kind in the space L2[a, b]. The nonlinear term will simply be handled with the help of Adomian polynomials. The Laplace decomposition technique is found to be fast and correct. Several examples are tested and also the results of the study are discussed. The obtained results expressly reveal the complete reliability, efficiency, and  accuracy of the proposed algorithmic rule for solving the Fredholm–Volterra integro–differential equations and therefore will be extended to other problems of numerous nature