Taylor Series Method with Numerical Derivatives …

Taylor Series Method with Numerical Derivatives forNumerical Solution of ODE Initial Value ProblemsE. MileticsG. Moln arkaDepartment of Mathematics, Sz echenyi Istv an University, Gy ISSN 1418-7108:HEJ Manuscript no.: ANM-030110-BAbstractThe Taylor Series Method is one of the earliest analytic-numeric algorithms forapproximate solution of initial value problems for ordinary differential this algorithm is not applied frequently. This is because when one solvessystems of ordinary differential equations, calculating the higher order derivativesformally is an over-elaborate task, this is true even if one uses the computer algebraicsystems such as MATHEMATICA or MAPLEV. The other reason is that only theexplicit versions of this algorithm are known. The main idea of the rehabilitation ofthese algorithms is based on the approximate calculation of higher Derivatives us-ing well-known technique for the partial differential equations.

Taylor Series Method with Numerical Derivatives for Numerical Solution of ODE Initial Value Problems E. Miletics G. Moln´arka Department of Mathematics, Sz´echenyi Istv´an University, Gy˝or

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  Series, With, Solutions, Methods, Numerical, Derivatives, Series method with numerical derivatives, Series method with numerical derivatives for numerical solution

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