### Pseudo-Runge-Kutta Methods Involving Two PointsPseudo-Runge-Kutta Methods Involving Two Points

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 Author Byrne, George D. ♦ Lambert, Robert J. Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1966 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Abstract A third order two step method and a fourth order two step method for the numerical solution of the vector initial value problem $\textit{dy}$ ÷ $\textit{dx}=F(y),$ $y(\textit{a})$ = n can be defined by making evaluations of F similar to those found in a classical Runge-Kutta formula. These two step methods are different from classical Runge-Kutta methods in that evaluations of F made at the previous point are used along with those made at the current point in order to obtain the solution at the next point. If the stepsize is fixed, this use of previous computations makes it possible to obtain the solution at the next point by evaluating F two or three times for the third or fourth order method, respectively.These methods are consistent with the initial value problem and are shown to be convergent with its unique solution under certain restrictions. The local truncation error terms are given. Finally, a few numerical results are presented. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1966-01-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 13 Issue Number 1 Page Count 10 Starting Page 114 Ending Page 123

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Source: ACM Digital Library