Journal Article10.1007/BF01931218
Finite difference methods for two-point boundary value problems involving high order differential equations
M. M. Chawla,C. P. Katti +1 more
126
TL;DR: In this paper, the construction of finite difference schemes for (2n+1)-diagonal linear systems was discussed, and convergence of these methods was established and illustrated by numerical examples.
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Abstract: We discuss the construction of finite difference schemes for the two-point nonlinear boundary value problem:y
(2n)+f(x,y)=0,y
(2j)(a)=A
2j
,y
(2j)(b)=B
2j
,j=0(1)n−1,n≧2. In the case of linear differential equations, these finite difference schemes lead to (2n+1)-diagonal linear systems. We consider in detail methods of orders two, four and six for two-point boundary value problems involving a fourth order differential equation; convergence of these methods is established and illustrated by numerical examples.
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Citations
Approximate solutions to boundary value problems of higher order by the modified decomposition method
TL;DR: In this paper, an efficient numerical algorithm for approximate solutions of higher-order boundary value problems with two-point boundary conditions is presented. But the algorithm is based on a modified form of the Adomian decomposition method.
187
Homotopy Perturbation Method for Solving Fourth-Order Boundary Value Problems
TL;DR: In this paper, the homotopy perturbation method was applied for solving the fourth-order boundary value problems and the analytical results were obtained in terms of convergent series with easily computable components.
Variational iteration technique for solving higher order boundary value problems
TL;DR: Higher order boundary value problems can be written as a system of integral equations, which can be solved by using the variational iteration technique, which is considered as alternative and efficient for finding the approximate solutions of the boundary values problems.
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The numerical solution of sixth-order boundary value problems by the modified decomposition method
TL;DR: A fast and accurate algorithm is developed for the solution of sixth-order boundary value problems (BVPs) with two-point boundary conditions using a modified form of the Adomian decomposition method.
149
Homotopy perturbation method for solving sixth-order boundary value problems
TL;DR: This paper applies the homotopy perturbation method for solving the sixth-order boundary value problems by reformulating them as an equivalent system of integral equations by using a suitable transformation.
138
References
On the numerical integration of a boundary value problem involving a fourth order linear differential equation
TL;DR: In this paper, a finite difference method for the numerical integration of the linear two-point boundary value problem is presented, which requires only the solution of linear equations associated with a five-band matrix.
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