Three different spline-based approaches for solving Bratu and Bratu-type equations are presented. The classical cubic spline collocation method, an adaptive spline collocation on nonuniform partitions, and an optimal collocation method are derived for solving Bratu-type equations. Numerical examples are presented to verify the efficiency and accuracy of these methods when compared to other nume...

in the present article, a numerical method is proposed for the numerical solution of thekdv equation by using a new approach by combining cubic b-spline functions. in this paper we convert the kdv equation to system of two equations. the method is shown to be unconditionally stable using von-neumann technique. to test accuracy the error norms2l, ∞l are computed. three invariants of motion are p...

‎in this paper we introduce a numerical approach that solves optimal control problems (ocps)‎‎using collocation methods‎. ‎this approach is based upon b-spline functions‎.‎the derivative matrices between any two families of b-spline functions are utilized to‎‎reduce the solution of ocps to the solution of nonlinear optimization problems‎.‎numerical experiments confirm our theoretical findings‎.

we develope a numerical method based on b-spline collocation method to solve linear klein-gordon equation. the proposed scheme is unconditionally stable. the results of numerical experiments have been compared with the exact solution to show the efficiency of the method computationally. easy and economical implementation is the strength of this approach.

. In this paper, we develop a quadratic spline collocation method for integrating the nonlinear partial differential equations (PDEs) of a plug flow reactor model. The method is proposed in order to be used for the operation of control design and/or numerical simulations. We first present the Crank-Nicolson method to temporally discretize the state variable. Then, we develop and analyze the pro...

The variation in the accuracy of the calculated natural frequencies of pre-twisted beams solved with spline collocation method is investigated in this study. The spline collocation method is used to formulate the eigenvalue problems of pre-twisted beams. Three types of boundary conditions are considered. Numerical results indicate that the accuracy of the calculated natural frequencies is signi...

The natural frequencies of non-uniform beams resting on elastic foundations are numerically obtained using the spline collocation procedure. The spline collocation method is a numerical approach effective at solving partial differential equations. The boundary conditions that accompanied the spline collocation procedure were used to convert the partial differential equations of non-uniform beam...

The numerical stability of the polynomial spline collocation method for general Volterra integro-differential equation is being considered. The convergence and stability of the newmethod are given and the efficiency of the newmethod is illustrated by examples. We also proved the conjecture suggested by Danciu in 1997 on the stability of the polynomial spline collocation method for the higher-or...

In this paper, we improve b-spline collocation method for Benjamin-Bona-Mahony-Burgers (BBMB) by using defect correction principle. The exact finite difference scheme is used to find defect and the defect correction principle is used to improve collocation method. The method is tested on somemodel problems and the numerical results have been obtained and compared.

Quartic-Spline Collocation Methods for Fourth-Order Two-Point Boundary Value Problems Ying Zhu Master of Science Graduate Department of Computer Science University of Toronto 2001 This thesis presents numerical methods for the solution of general linear fourth-order boundary value problems in one dimension. The methods are based on quartic splines, that is, piecewise quartic polynomials with C3...