The aim of the present paper is to present a numerical algorithm for the time-dependent generalized regularized long wave equation with boundary conditions. We semi-discretize the continuous problem by means of the Crank–Nicolson finite difference method in the temporal direction and exponential B-spline collocation method in the spatial direction. The method is shown to be unconditionally stab...

Abstract. We present a new modified nodal cubic spline collocation scheme for solving the Dirichlet problem for Poisson’s equation on the unit square. We prove existence and uniqueness of a solution of the scheme and show how the solution can be computed on an (N + 1) × (N + 1) uniform partition of the square with cost O(NlogN) using a direct fast Fourier transform method. Using two comparison ...

In this study, we present numerical methods, based on the optimal quadratic spline collocation (OQSC) methods, for solving the shallow water equations (SWEs) in spherical coordinates. A quadratic spline collocation method approximates the solution of a differential problem by a quadratic spline. In the standard formulation, the quadratic spline is computed by making the residual of the differen...

In this paper, we construct a numerical ‎method‎ to ‎the ‎solution ‎of‎ the Black-Scholes partial differential equation modeling the European option pricing problem with regard to a single asset‎. ‎W‎e use an explicit spline-difference scheme which is based on using a finite difference approximation for the temporal derivative and a cubic B-spline collocation for spatial derivatives. ‎The deriv...

In this study, a new algorithm is introduced for the numerical solution of equal width (EW) equation. This created by using collocation finite element method based on decic B-spline functions space discretization EW equation and Crank-Nicolson time his The obtained results are compared with previous ones to see efficiency accuracy proposed method.

Abstract—In this paper, numerical solution of system of Fredholm and Volterra integral equations by means of the Spline collocation method is considered. This approximation reduces the system of integral equations to an explicit system of algebraic equations. The solution is collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. The error analysis of propose...