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Block methods based on Newton interpolations for solving special second order ordinary differential equations directly. (English) Zbl 1186.65088
Summary: We are focused mainly on the derivation of 2 and 3-point block methods with constant coefficients for solving special second order ordinary differential equations directly based on the Newton-Gregory backward interpolation formula. The performance of the new methods was compared with the conventional 1-point method using a standard set of test problems. Numerical results are presented to illustrate the effectiveness of the methods in terms of the total number of steps taken, maximum error and execution time. The results suggest a significant improvement in efficiency of the r-point block method.
MSC:
65L05Initial value problems for ODE (numerical methods)