ORDER AND STABILITY OF THE REFORMULATED HYBRID BLOCK METHOD FOR SOLVING NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS
Keywords:
Hybrid, Block Method, Stiff, Order, zero stable, A-StableAbstract
In this paper, the order and stability analysis of the hybrid variable step size block method for solving nonlinear ordinary differential equation is established. The scheme adopted a variable step size technique. The new hybrids block method for solving stiff ODEs developed by Sagir et. al., are re-derived by introducing a variable step size ratio (r), r=1/5 to obtained a stable method. However, the paper focuses on analysing the order and stability of the new stable method, by establishing the necessary and sufficient condition for order and stability. The method is found to satisfy the entire criteria for order and Stability, so the scheme is consistent, Zero stable and A-Stable capable of solving stiff nonlinear initial value problems. Existing Stiff Nonlinear Ordinary Differential Equations is solved using the method and the numerical result obtained using the new method are found to be efficient at certain step sizes. Hence, the new scheme is recommended for the solution of stiff Nonlinear Ordinary Differential Equations.References
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