Riaz A. Usmani
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View article: Numerical solution of boundary value problems in ordinary differential equations
Numerical solution of boundary value problems in ordinary differential equations Open
In the numerical solution of the two point "boundary value problem, [ equation omitted ] (1) the usual method is to approximate the problem by a finite difference analogue of the form [ equation omitted ] (2) with k = 2, and the truncation…
View article: Two new finite difference methods for computing eigenvalues of a fourth order linear boundary value problem
Two new finite difference methods for computing eigenvalues of a fourth order linear boundary value problem Open
This paper describes some new finite difference methods of order 2 and 4 for computing eigenvalues of a two‐point boundary value problem associated with a fourth order differential equation of the form . Numerical results for two typical e…
View article: Finite difference methods for computing eigenvalues of fourth order boundary value problems
Finite difference methods for computing eigenvalues of fourth order boundary value problems Open
This brief report describes some new finite difference methods of order 2 and 4 for computing eigenvalues of a two point boundary value problem associated with a fourth order linear differential equation y (4) + ( p ( x ) − λ q ( x )) y = …
View article: Biquadratic Spline Approximations
Biquadratic Spline Approximations Open
We shall consider two kinds of spline approximations over a uniform mesh. The first of them is mid-point spline interpolation and the second is histospline approximation. Our methods don't need any knowledge of derivative values, that is, …
View article: Exponential quadratic splines
Exponential quadratic splines Open
On considere des splines quadratiques exponentielles et leurs relations de consistance parmi les valeurs de fonctions ou des derivees aux points de maillage et milieu
View article: Spline Solutions for Nonlinear Fourth-Order Two-Point Boundary Value Problems
Spline Solutions for Nonlinear Fourth-Order Two-Point Boundary Value Problems Open
Methods of order 2 and 4 are developed for the continuous approximation of thesolution of a nonlinear fourth-order two-point boundary value problem.Numerical results are briefly summarized to demonstrate the practical usefulness of the met…
View article: Quadratic Spline and Two-Point Boundary Value Problem
Quadratic Spline and Two-Point Boundary Value Problem Open
where f ( t , x, y) is defined and twice continuously differentiable in a region D of the (t, x} :y)-space intercepted by two hyperplanes £=0 and t=l. The analytical solution of (1.1) for arbitrary choices of the function / cannot be found…
View article: Asymptotic error estimation for spline-on-spline interpolation
Asymptotic error estimation for spline-on-spline interpolation Open
On considere l'estimation de l'erreur asymptotique pour l'interpolation spline sur spline sur un maillage uniforme
View article: Spline solutions for nonlinear two point boundary value problems
Spline solutions for nonlinear two point boundary value problems Open
Necessary formulas are developed for obtaining cubic, quartic, quintic, and sextic spline solutions of nonlinear boundary value problems. These methods enable us to approximate the solution of the boundary value problems, as well as their …
View article: A uniqueness theorem for a boundary value problem
A uniqueness theorem for a boundary value problem Open
In this paper it is proved that the two-point boundary value problem, namely , has a unique solution provided . The given boundary value problem is discretized by a finite difference scheme. This numerical approximation is proved to be a s…
View article: Discrete Variable Methods for a Boundary Value Problem with Engineering Applications
Discrete Variable Methods for a Boundary Value Problem with Engineering Applications Open
In this paper we develop numerical techniques of order 2, 4 and 6 for the solution of a fourth order linear equation. A priori error bound is obtained for the fourth order method to prove the convergence of the finite difference scheme. A …
View article: Boundary Value Techniques for the Numerical Solution of Certain Initial Value Problems in Ordinary Differential Equations
Boundary Value Techniques for the Numerical Solution of Certain Initial Value Problems in Ordinary Differential Equations Open
Linear initial value problems, particularly involving first order differential equations, can be transformed into systems of higher order and treated as boundary value problems. The type of difference equations used to replace the associat…