Theoretical Mathematics & Applications

A family of symmetric implicit higher order methods for the solution of third order initial value problems in ordinary differential equations

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• Abstract

  A family of higher order implicit methods with k-steps is constructed which was used to solve initial value problems of third order ordinary differential equations directly without reducing them to first order systems. Implicit methods with step numbers k=3, 4, 5 are considered. For these methods, we discussed the local truncation error with the basic properties. Analysis of the basic properties of the methods shows that the methods are consistent, convergent and zero – stable. The results obtained from numerical experiment shows that the methods are more efficient and accurate than some existing methods.