Evolutionary Generation of Runge-Kutta Pairs
نویسنده
چکیده
Y. G. Petalas1, Ch. Tsitouras2, G. S. Androulakis3, and M. N. Vrahatis ∗1 1 Computational Intelligence Laboratory (CI Lab), Department of Mathematics, University of Patras Artificial Intelligence Research Center (UPAIRC), University of Patras, GR–26110 Patras, Greece 2 Department of Applied Sciences, TEI of Chalkis, GR–34400 Psahna, Greece 3 Department of Business Administration, University of Patras, GR–26110 Patras, Greece
منابع مشابه
Singly diagonally implicit Runge-Kutta methods with an explicit first stage
The purpose of this paper is to construct methods for solving stiff ODEs, in particular singular perturbation problems. We consider embedded pairs of singly diagonally implicit Runge-Kutta methods with an explicit first stage (ESDIRKs). Stiffly accurate pairs of order 3/2, 4/3 and 5/4 are constructed. AMS Subject Classification: 65L05
متن کاملRunge-Kutta pairs of order 5(4) satisfying only the first column simplifying assumption
Among the most popular methods for the solution of the Initial Value Problem are the Runge–Kutta pairs of orders 5 and 4. These methods can be derived solving a system of nonlinear equations for its coefficients. For achieving this, we usually admit various simplifying assumptions. The most common of them are the so called row simplifying assumptions. Here we negligible them and present an algo...
متن کاملRunge-Kutta Pairs for Scalar Autonomous Initial Value Problems
We present the equations of condition up to sixth order for Runge-Kutta (RK) methods, when integrating scalar autonomous problems. Two RK pairs of orders 5(4) are derived. The first at a cost of only five stages per step, while the other having an extremely small principal truncation error. Numerical tests show the superiority of the new pairs over traditional ones.
متن کاملOn the Construction of Splitting Methods by Stabilizing Corrections with Runge-Kutta Pairs
In this technical note a general procedure is described to construct internally consistent splitting methods for the numerical solution of differential equations, starting from matching pairs of explicit and diagonally implicit Runge-Kutta methods. The procedure will be applied to suitable second-order pairs, and we will consider methods with or without a mass conserving finishing stage. For th...
متن کاملAdditive Runge-Kutta Methods for Stiff Ordinary Differential Equations
Certain pairs of Runge-Kutta methods may be used additively to solve a system of n differential equations x' = J(t)x + g(t, x). Pairs of methods, of order p < 4, where one method is semiexplicit and /(-stable and the other method is explicit, are obtained. These methods require the LU factorization of one n X n matrix, and p evaluations of g, in each step. It is shown that such methods have a s...
متن کامل