In this paper, we construct a new numerical algorithm for the partial differential equation of up-and-out put barrier options under CEV model. method, use Crank-Nicolson scheme to discrete temporal variables and cubic B-spline collocation method spatial variables. The is stable has second-order convergence both time space analysis proposed discussed in detail. Finally, examples verify stability...

A finite element method involving collocation method with Quintic B-splines as basis functions has been developed to solve fifth order boundary value problems. The fifth order derivative for the dependent variable is approximated by the finite differences. The basis functions are redefined into a new set of basis functions which in number match with the number of collocated points se lected in ...

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.

We present an exponential B-spline collocation method for solving convection-diffusion equation with Dirichlet’s type boundary conditions. The method is based on the Crank-Nicolson formulation for time integration and exponential B-spline functions for space integration. Using the Von Neumann method, the proposed method is shown to be unconditionally stable. Numerical experiments have been cond...