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Continuous Explicit Hybrid Method for Solving Second Order Ordinary Differential Equations
Pure and Applied Mathematics Journal
Volume 9, Issue 1, February 2020, Pages: 26-31
Received: Dec. 23, 2019; Accepted: Jan. 9, 2020; Published: Feb. 13, 2020
Authors
Friday Oghenerukevwe Obarhua, Department of Mathematical Sciences, School of Sciences, The Federal University of Technology, Akure, Nigeria
Sunday Jacob Kayode, Department of Mathematical Sciences, School of Sciences, The Federal University of Technology, Akure, Nigeria
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Abstract
This paper presents an explicit hybrid method for direct approximation of second order ordinary differential equations. The approach adopted in this work is by interpolation and collocation of a basis function and its corresponding differential system respectively. Interpolation of the basis function was done at both grid and off-grid points while the differential systems are collocated at selected points. Substitution of the unknown parameters into the basis function and simplification of the resulting equation produced the required continuous, consistent and symmetric explicit hybrid method. Attempts were made to derive starting values of the same order with the methods using Taylor’s series expansion to circumvent the inherent disadvantage of starting values of lower order. The methods were applied to solve linear, non-linear, Duffing equation and a system of equation second-order initial value problems directly. Errors in the results obtained were compared with those of the existing implicit methods of the same and even of higher order. The comparison shows that the accuracy of the new method is better than the existing methods.
Keywords
Continuous, Duffing Equation, Explicit, Symmetric, Zero-stable, Approximate Solution, Power Series
Friday Oghenerukevwe Obarhua, Sunday Jacob Kayode, Continuous Explicit Hybrid Method for Solving Second Order Ordinary Differential Equations, Pure and Applied Mathematics Journal. Vol. 9, No. 1, 2020, pp. 26-31. doi: 10.11648/j.pamj.20200901.14
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