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Numerical Solution of Linear Second Order Ordinary Differential Equations with Mixed Boundary Conditions by Galerkin Method
Mathematics and Computer Science
Volume 2, Issue 5, September 2017, Pages: 66-78
Received: Apr. 28, 2017; Accepted: Jun. 6, 2017; Published: Sep. 18, 2017
Authors
Akalu Abriham Anulo, Department of Mathematics, Institute of Technology, Dire Dawa University, Dire Dawa, Ethiopia
Alemayehu Shiferaw Kibret, Department of Mathematics, Jimma University, Jimma, Ethiopia
Genanew Gofe Gonfa, Department of Mathematics, Jimma University, Jimma, Ethiopia
Ayana Deressa Negassa, Department of Mathematics, Jimma University, Jimma, Ethiopia
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Abstract
In this paper, the Galerkin method is applied to second order ordinary differential equation with mixed boundary after converting the given linear second order ordinary differential equation into equivalent boundary value problem by considering a valid assumption for the independent variable and also converting mixed boundary condition in to Neumann type by using secant and Runge-Kutta methods. The resulting system of equation is solved by direct method. In order to check to what extent the method approximates the exact solution, a test example with known exact solution is solved and compared with the exact solution graphically as well as numerically.
Keywords
Second Order Ordinary Differential Equation, Mixed Boundary Conditions, Runge-Kutta, Secant Method, Galerkin Method, Chebyshev Polynomials
Akalu Abriham Anulo, Alemayehu Shiferaw Kibret, Genanew Gofe Gonfa, Ayana Deressa Negassa, Numerical Solution of Linear Second Order Ordinary Differential Equations with Mixed Boundary Conditions by Galerkin Method, Mathematics and Computer Science. Vol. 2, No. 5, 2017, pp. 66-78. doi: 10.11648/j.mcs.20170205.12
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