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Home  >  Volume 28. No.2 (Nov. 2014)

20. Chebyshev Collocation Approach for Continuous Two-Step Hybrid Block Method for the Solution of First Order... by R. B. Adeniyi and N. S. Yakusak - Volume28, No. 2, (November, 2014), pp 141 – 150
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The numerical solution of initial value problem of  general first order Ordinary Differential Equation has been studied in this work. A continuous two-step hybrid block method capable of solving this class of problems has been developed using collocation and interpolation techniques and with Chebyshev polynomial as basis function. The two-step method was augmented by the  introduction of offstep points that guaranteed zero stability. The continuous hybrid block two-step methods has the advantage of easy change of step length and evaluation of functions at offstep points. Numerical examples are presented to illustrate the accuracy and effectiveness of the method. Keywords:Interpolation, Chebyshev polynomial, Collocation, and Continuous scheme.