NUMERICAL SOLUTION OF SECOND ORDER DIFFERENTIAL EQUATIONS USING RATIONAL PADE CONVERGENTS.
NAVAL POSTGRADUATE SCHOOL MONTEREY CA
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Rational Pade convergents to a function of the forward shift operator F are computed from coefficients of its power series expansion. These Pade convergents are used to generate recursion formulas which are then employed to obtain approximate numerical solutions of several second order differential equations. A variety of integration step lengths are used. Solution error is plotted against the number of iteration steps and results are evaluated. It is concluded that this procedure is beneficial as a method of deriving corrector formulas to be used in the predictor-corrector method of solving second order differential equations. A method for deriving improved predictor formulas is suggested. Author
- Numerical Mathematics