non-polynomial spline solutions for special nonlinear fourth-order boundary value problems
Authors
abstract
we present a sixth-order non-polynomial spline method for the solutions of two-point nonlinear boundary value problem u(4)+f(x,u)=0, u(a)=α1, u''(a)= α2, u(b)= β1,u''(b)= β2, in off step points. numerical method of sixth-order with end conditions of the order 6 is derived. the convergence analysis of the method has been discussed. numerical examples are presented to illustrate the applications of method, and to compare the computedresults with other known methods.
similar resources
NON-POLYNOMIAL SPLINE SOLUTIONS FOR SPECIAL NONLINEAR FOURTH-ORDER BOUNDARY VALUE PROBLEMS
We present a sixth-order non-polynomial spline method for the solutions of two-point nonlinear boundary value problem u(4)+f(x,u)=0, u(a)=α1, u''(a)= α2, u(b)= β1,u''(b)= β2, in off step points. Numerical method of sixth-order with end conditions of the order 6 is derived. The convergence analysis of the method has been discussed. Numerical examples are presented to illustrate the applications ...
full textNon polynomial spline solutions for special linear tenth-order boundary value problems
Non-polynomial spline is used for solution of the tenth-order linear boundary value problems. We obtained the classes of numerical methods for a specific choice of the parameters involved in non-polynomial spline. The end conditions consistent with the boundary value problems are derived. Truncation errors are given. A new approach convergence analysis of the presented methods is discussed. Two...
full textQuintic Spline Solutions of Fourth Order Boundary-value Problems
In this paper Quintic Spline is defined for the numerical solutions of the fourth order linear special case Boundary Value Problems. End conditions are also derived to complete the definition of spline.The algorithm developed approximates the solutions, and their higher order derivatives of differential equations. Numerical illustrations are tabulated to demonstrate the practical usefulness of ...
full textExistence of positive solutions for fourth-order boundary value problems with three- point boundary conditions
In this work, by employing the Krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime pri...
full textNON-POLYNOMIAL QUARTIC SPLINE SOLUTION OF BOUNDARY-VALUE PROBLEM
Quartic non-polynomial spline function approximation in off step points is developed, for the solution of fourth-order boundary value problems. Using consistency relation of such spline and suitable choice of parameter,we have obtained second, fourth and sixth orders methods. Convergence analysis of sixth order method has been given. The methods are illustrated by some examples, to verify the or...
full textApproximations for Linear Tenth-order Boundary Value Problems through Polynomial and Non-polynomial Cubic Spline Techniques
Higher order differential equations have always been a tedious problem to solve for the mathematicians and engineers. Different numerical techniques were carried out to obtain numerical approximations to such problems. This research work presented and illustrated a novel numerical technique to approximate the tenth-order boundary value problems (BVPs). The techniques developed in this research ...
full textMy Resources
Save resource for easier access later
Journal title:
international journal of mathematical modelling and computationsجلد ۱، شماره ۲ (SPRING)، صفحات ۱۳۵-۱۴۷
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023