A numeric-analytical method for solving the Cauchy problem for ordinary differential equations
arXiv:1009.005812 citationsh-index: 13
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For researchers working on numerical solutions of ODEs, this offers an alternative method with improved convergence properties.
The paper proposes a functional-discrete method for solving the Cauchy problem for first-order ODEs, which converges for some problems where the Adomian Decomposition Method diverges.
In the paper we offer a functional-discrete method for solving the Cauchy problem for the first order ordinary differential equations (ODEs). This method (FD-method) is in some sense similar to the Adomian Decomposition Method. But it is shown that for some problems FD-method is convergent whereas ADM is divergent. The results presented in the paper can be easily generalized on the case of systems of ODEs.