A Numerical Approach to the Solution of the System of Second-Order Boundary-Value Problems
galerkin method, bernstein polynomials, numerical solution of system of second order BVPs
Abstract
In this paper, Galerkin method is presented to obtain the approximate solutions of the system of second order boundary value problems using piecewise continuous and differentiable Bernstein polynomials. Derivation of rigorous matrix formulations is exploited to solve the system of second order boundary value problems where, given boundary conditions are satisfied by Bernstein polynomials. The derived formulation is applied to solve the system of second order boundary value problems numerically. Results of numerical approximate solutions converge to the exact solutions monotonically with desired large significant accuracy.
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H Thompson, Christopher Tisdell (2000) Systems of Difference Equations Associated with Boundary Value Problems for Second Order Systems of Ordinary Differential Equations. 248(2), 333-347.
Xiyon Cheng, Chengkui Zhong (2005) Existence of positive solutions for a second order ordinary differential system. 312, 14-23.
H Thompson, C Tisdell (2002) Boundary value problems for systems of difference equations associated with systems of second-order ordinary differential equations. 15(6), 761-766.
H Thompson, C Tisdell (2003) The nonexistence of spurious solutions to discrete, two-point boundary value problems. 16(1), 79-84.
Ali Sayfy, S Khoury (2012) A fourth-order spline collocation approach for the numerical solution of a generalized system of second-order boundary-value problems. 1734-1738.
J Mawhin, C Tisdell (2003) A note on the uniqueness of solutions to nonlinear, discrete, vector boundary value problems. 1(2), 789-798.
T Valanarasu, N Ramanujam (2004) An asymptotic initial value method for boundary value problems for a system of singularly perturbed second order ordinary differential equations. 147(1), 227-240.
Fazhan Geng, Minggen Cui (2007) Solving a nonlinear system of second order boundary value problems. 327(2), 1167-1181.
M Bhatti, P Braken (2007) Solutions of differential equations in a Bernstein Polynomial basis. 205, 272-280.
J Reinkenhof (1977) Differentiation and integration using Bernstein's polynomials. 11, 1627-1630.
Erwin Kreyszig (1979) Bernstein polynomials and numerical integration. 14(2), 292-295.
Jungfeng Lu (2007) Variational iteration method for solving a nonlinear system of second-order boundary value problems. 54(7-8), 1133-1138.
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2019-02-06
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