Generalized Predictor‐Corrector Methods of High Order for the Time Integration of Parabolic Differential Equations

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Abstract
A general class of predictor‐corrector methods is presented and explicit expressions for the local truncation error and the stability polynomial are derived. Examples of methods of orders up to 6 are given which are suitable for the integration of semi‐discrete parabolic differential equations. By a large number of numerical experiments we show that the higher order methods are generally more efficient than the lower order methods. As a further illustration we compare the generalized predictor‐corrector methods with the familiar ADI Method confirming our general belief that for smooth parabolic problems high order time integrators are superior to lower order integrators.

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