Abstract
AbstractThe 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.
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