A Superexponentially Convergent Functional-Discrete Method for Solving the Cauchy Problem for Systems of Ordinary Differential Equations
For researchers solving ODE systems, this method offers faster convergence, but it is incremental as it builds on existing FD-method and Adomian polynomials.
The paper presents a new numerical-analytical method for solving the Cauchy problem for systems of ODEs, achieving superexponential convergence. Numerical examples show it outperforms the Adomian Decomposition Method.
In the paper a new numerical-analytical method for solving the Cauchy problem for systems of ordinary differential equations of special form is presented. The method is based on the idea of the FD-method for solving the operator equations of general form, which was proposed by V.L. Makarov. The sufficient conditions for the method converges with a superexponential convergence rate were obtained. We have generalized the known statement about the local properties of Adomian polynomials for scalar functions on the operator case. Using the numerical examples we make the comparison between the proposed method and the Adomian Decomposition Method.