A Method for the Integration in Time of Certain Partial Differential Equations

Abstract A method for the numerical solution of ordinary differential equations is analyzed that is explicit and yet can conserve the quadratic quantities conserved by the equations. The method can be a useful alternative to the usual leapfrog technique, in that it does not suffer from the occurrence of blowup phenomena. Numerical examples concerning the Korteweg-de Vries equation and the nonlinear Schrodinger equation are given.

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