A NEW 3RD-ORDER FINITE-DIFFERENCE METHOD FOR TRANSIENT ONE-DIMENSIONAL ADVECTION DIFFUSION

The accuracy of some first- and second-order methods for solving the time-dependent one-dimensional constant-coefficient advection-diffusion equation are compared theoretically on the basis of the dominant error terms in their modified equivalent partial differential equations. A new very stable three-point (in space) third-order implicit method is then developed by combining two second-order methods. The accuracies of the various methods are then compared by means of numerical tests.