A Compact Quadratic Spline Collocation Method for the Convection-diffusion Equation

Based on the quadratic spline interpolation functions, an optimal compact quadratic spline collocation method is presented for the convection-diffusion equation. As for The said method, first by use of quadratic spline basis function, discret- ization is done in the space direction, thus the problem is transformed into a series of ordinary differential equation. Then, the classical fourth-order Runge-Kutta method and Trapezoid formula are respectively employed to determine the iterative solution and with experiments the numerical stability of the method is compared and analyzed. Numerical examples find that the presen- ted collocation scheme can achieve fourth-order accuracy in space no matter which kind of iterative method is used."