Paper Type |
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Research Paper |
Title |
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Uniform Order Continuous Block Hybrid Method for the Solution of First Order Ordinary Differential Equations |
Country |
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Nigeria. |
Authors |
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A.A. James,A.O. Adesanya,J. Sunday |
 |
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10.9790/5728-0360814  |
Abstract :We know that for any numerical method to be efficient and computational reliable, it must be convergent, consistent, and stable. This paper adopted the method of interpolation of the approximate solution and collocation ofits differential system at grid and off grid points to yield a continuous linear multistep method with a constant step size. The continuous linear multistep method is solved for the independent solution to yield a continuous block method which is evaluated at selected grid and off grid points to yield a discrete block method. The basic property of this method is verified to be convergent consistent and satisfies the conditions for stability. The method was tested on numerical examples and found to compete favorably withthe existing methods in term of accuracy and error variation.
Keywords: interpolation, IVP, ODEs, colocation, approximate solution, independent solution, block method, convergent.
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