‎‎‎In this paper‎, we use the collocation method for to find an approximate solution of the problem by cubic B-spline basis.‎ The proposed method as a basic function led matrix systems, including band matrices and smoothness and capability to handle low calculative costly. ‎The absolute errors in the solution are compared to existing methods to verify the accuracy and convergent nature of propo...

The famous de Boor conjecture states that the condition of the polynomial B-spline collocation matrix at the knot averages is bounded independently of the knot sequence, i.e., it depends only on the spline degree. For highly nonuniform knot meshes, like geometric meshes, the conjecture is known to be false. As an effort towards finding an answer for uniform meshes, we investigate the spectral c...

In the present study, we derive a new B-spline technique namely trigonometric B-spline collocation algorithm to solve some initial boundary value problems for the nonlinear Klein-Gordon equation. In order to carry out the time integration with Crank-Nicolson implicit method, the order of the equation is reduced to give a coupled system of nonlinear partial differential equations. The collocatio...

Powell–Sabin splines are piecewise quadratic polynomials with a global C1-continuity, defined on conforming triangulations. Imposing boundary conditions on such a spline leads to a set of constraints on the spline coefficients. First, we discuss boundary conditions defined on a polygonal domain, before we treat boundary conditions on a general curved domain boundary. We consider Dirichlet and N...

Nowadays, options are common financial derivatives. For this reason, by increase of applications for these financial derivatives, the problem of options pricing is one of the most important economic issues. With the development of stochastic models, the need for randomly computational methods caused the generation of a new field called financial engineering. In the financial engineering the pre...

In this paper, an Adomian decomposition method using Chebyshev orthogonal polynomials is proposed to solve a well-known class of weakly singular Volterra integral equations. Comparison with the collocation method using polynomial spline approximation with Legendre Radau points reveals that the Adomian decomposition method using Chebyshev orthogonal polynomials is of high accuracy and reduces th...

A collocation procedure is developed for the linear and nonlinear Fredholm and Volterra integro-differential equations, using the globally defined B-spline and auxiliary basis functions.The solution is collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. The error analysis of proposed numerical method is studied theoretically. Numerical results are given t...

In this paper, a high-order method for solving the Schrodinger equation is introduced. We apply a compact finite difference approximation for discretizing spatial derivatives and we use the C-cubic spline collocation method for the time integration of the resulting linear system of ordinary differential equations. The proposed method has fourth-order accuracy in both space and time variables. W...

In this paper, a spline finite element approach is manipulated for the numerical solution of an extended system of second-order boundaryvalue problems. The efficiency of the proposed method is examined by comparing the results with the existing exact closed form solution. The numerical results demonstrate that the method is efficient and quite accurate when contrasted with other methods and req...

In this article, the cubic B-spline collocation method is implemented to find numerical solution of the problem arising from chemical reactor theory. The method is tested on some model problems from the literature, and the numerical results are compared with other methods.