β Scribed by H.E. Heatherly
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The Maclaurin transform (or generating function method) is generalized to have as its range a ring of formal power series. All the usual operations needed for solving difference equations via this method are then carried out in the quotient division algebra of this ring. This allows one to solve difference equations whose solutions exhibit arbitrarily rapid growth. The method is illustrated with two specific examples.
π SIMILAR VOLUMES
A systematic method for searching travelling-wave solutions to differential-difference equations (DDEs) is proposed in the paper. First of all, we introduce BΓ€cklund transformations for the standard Riccati equation which generate new exact solutions by using its simple and known solutions. Then we
Classical finite difference schemes are in wide use today for approximately solving partial differential equations of mathematical physics. An evolution of the method of finite differences has been the development of generalized finite difference (GFD) method, that can be applied to irregular grids