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Initial Value Solvers for Second Order Ordinary Differential Equations Using Chebyshev Polynomial as Basis Functions

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Abstract:

Direct numerical solutions of second and higher order ODEs have constituted a major problem in the resent past. In order to seek for numerical solution of equations of these types, one have to resolve the equations into a system of first order ordinary differential equations before solving the resulting equations with any desired known methods. In an attempt to do this, it often takes a very long period of time and the task is always laborious. In order to circumvent this problem, we were led to this present study. Here, we decide to come up with a multistep method which is more accurate and more efficient with very small error constant in solving second order ordinary differential equations without resolving into system of first order ordinary differential equations. The method used here is based on collocating and interpolating at k and k-1 points respectively where k = 6. This yields a 6 step method which is symmetric, zero stable and constituent. Some numerical examples were given to illustrate the desirability and efficiency of this method.

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