A Metaheuristic Optimization Algorithm for Solving Higher-Order Boundary Value Problems

An ${cal O}(h^{8})$ optimal B-spline collocation for solving higher order boundary value problems

As we know the approximation solution of seventh order two points boundary value problems based on B-spline of degree eight has only ${cal O}(h^{2})$ accuracy and this approximation is non-optimal. In this work, we obtain an optimal spline collocation method for solving the general nonlinear seventh order two points boundary value problems. The ${cal O}(h^{8})$ convergence analysis, mainly base...

An efficient algorithm for solving fifth-order boundary value problems

In this paper, we apply the homotopy perturbation method for solving the fifth-order boundary value problems. The analytical results of the equations have been obtained in terms of convergent series with easily computable components. Several examples are given to illustrate the efficiency and implementation of the homotopy perturbation method. Comparisons are made to confirm the reliability of ...

Boundary value problems for higher order parabolicequationsRussell

Higher order multi-point fractional boundary value problems with integral boundary conditions

In this paper, we concerned with positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions. We establish the criteria for the existence of at least one, two and three positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions by using a result from the theory of fixed...

Singular Discrete Higher Order Boundary Value Problems

We study singular discrete nth order boundary value problems with mixed boundary conditions. We prove the existence of a positive solution by means of the lower and upper solutions method and the Brouwer fixed point theorem in conjunction with perturbation methods to approximate regular problems. AMS subject classification: 39A10, 34B16.