Abstarct: In this thesis, we solve partial differential equations with initial conditions and boundary conditions using B-spline function. At first, we introduce the partial differential equations and B-spline function.Then the collocation method using quartic B-splines is described for the numerical solutions of the Burgers’ equation and we solved the Burgers’ equation with septic b-splines and collocation method. In chapter 3 and 4 we use a numerical method baxsed on B-spline function and collocation method to solve second-order linear hyperbolic telegraph equation.In chapter 5, the telegraph equation is solved numerically by cubic B-spline quasi-interpolation.Finally the quartic B-spline collocation scheme is implemented to find numerical solution of the nonlinear fornberg-Whitham equation. At the end of each chapter the efficiency of the mentioned methods are showed by several numerical examples. Note that we have computed the numerical results by Matlab programming.