Solving third order boundary value problem using fourth order block method

A Novel Finite Difference Method of Order Three for the Third Order Boundary Value Problem in ODEs

In this article we have developed third order exact finite difference method for the numerical solution of third order boundary value problems. We constructed our numerical technique without change in structure of the coefficient matrix of the second-order method in cite{Pand}. We have discussed convergence of the proposed method. Numerical experiments on model test problems approves the simply...

Iterative method for solving a nonlinear fourth order boundary value problem

In the study of transverse vibrations of a hinged beam there arises a boundary value problem for fourth order ordinary differential equation, where a significant difficulty lies in a nonlinear term under integral sign. In recent years several authors considered finite approximation of the problem and proposed an iterative method for solving the system of nonlinear equations obtained. The essenc...

A spline method for solving fourth order singularly perturbed boundary value problem

In this paper, singularly perturbed boundary value problem of fourth order ordinary differential equation with a small positive parameter multiplying with the highest derivative of the form εu(4)(x) + p(x)u ′′ (x) + q(x)u(x) = r(x), 0 ≤ x ≤ 1, u(0) = γ0, u(1) = γ1, u ′′ (0) = η0, u ′′ (1) = η1, 0 ≤ ε ≤ 1 is considered. We have developed a numerical technique for the above problem using parametr...

Solving the non linear system of third order boundary value problems by using He's homotopy perturbation method

SOLVING LINEAR SIXTH-ORDER BOUNDARY VALUE PROBLEMS BY USING HYPERBOLIC UNIFORM SPLINE METHOD

In this paper, a numerical method is developed for solving a linear sixth order boundaryvalue problem (6VBP ) by using the hyperbolic uniform spline of order 3 (lower order). Thereis proved to be first-order convergent. Numerical results confirm the order of convergencepredicted by the analysis.