CRITICAL STUDY OF A NONLINEAR NUMERICAL SCHEME FOR INITIAL VALUE PROBLEMS

S. QURESHI, A. A. SHAIKH, M. S. CHANDIO

Abstract


The present paper aims at analyzing a nonlinear explicit one-step method to find numerical solutions of initial value problems (IVPs) in ordinary differential equations  (ODEs). Analysis  of  the  proposed  method  asserts  that  the  method is second order accurate with A-stability based upon ()11,−Padé approximation to the exponential functionze, contradicting claim of method’s developer about the method to have first order accuracy. Present study also discusses essential characteristics of the method that are observed to be missing in the original findings. Error analysis carried out also affirms second order accuracy of the method. Numerical results of some continuous mechanical and physical systems have been compared with both exact solutions (if possible) and solutions obtained from past methods in order to ascertain effectiveness of the method particularly with regard to order of accuracy.

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