A LOCAL COLLOCATION METHOD BASED ON GAUSSIAN RADIAL BASIS FUNCTION IS DEVELOPED FOR SOLUTION OF STEADY STATE TWO DIMENSIONAL CONVECTION- DIFFUSION EQUATION. CONSEQUENTLY THE ARISING SYSTEM IS SPARSE, WHICH IS AN EFFORT TO REDUCE THE CONDITION NUMBER OF THE SYSTEM AND TO OVERCOME THE ILL- CONDITIONING. THIS APPROACH IS SUITABLE FOR SOLVING PROBLEMS IN HIGH DIMENSIONAL TOO.

IN THIS PAPER, SINC-COLLOCATION METHOD IS USED FOR TIME-DEPENDENT CONVECTIONDIFFUSION EQUATIONS. SINC-COLLOCATION METHOD BASED ON DOUBLE EXPONENTIAL TRANSFORMATION ( DE) IS USED FOR SPACE DIMENSION AND FINITE DIFFERENCE METHOD IS USED FOR TIME DIMENSION. THE ERROR IN THE APPROXIMATION OF THE SOLUTION IS SHOWN TO CONVERGE AT AN EXPONENTIAL RATE, AND THE NUMERICAL RESULTS CONFIRM THAT COMPARED WITH THE RESULTS BASED ON SINGLE EXPONENTIAL TRANSFORMATION (SE), OUR METHOD IS OF HIGH ACCURACY AND OF GOOD CONVERGENCE.