Runge-Kutta pairs of order 5(4) satisfying only the first column simplifying assumption
نویسنده
چکیده
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 algorithm for the construction of Runge–Kutta pairs of orders 5 and 4 based only in the first column simplifying assumption. The result is a pair that outperforms other known pairs in the bibliography when tested to standard set of problems of DETEST. A cost free fourth order formula is also derived for handling dense output.
منابع مشابه
A family of fifth-order Runge-Kutta pairs
The construction of a Runge-Kutta pair of order 5(4) with the minimal number of stages requires the solution of a nonlinear system of 25 order conditions in 27 unknowns. We define a new family of pairs which includes pairs using 6 function evaluations per integration step as well as pairs which additionally use the first function evaluation from the next step. This is achieved by making use of ...
متن کاملSingly 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 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 کاملPartitioned Runge-kutta Methods for Separable Hamiltonian Problems
Separable Hamiltonian systems of differential equations have the form dp/dt = -dH/dq, dq/dt = dH/dp, with a Hamiltonian function H that satisfies H = T(p) + K(q) (T and V are respectively the kinetic and potential energies). We study the integration of these systems by means of partitioned Runge-Kutta methods, i.e., by means of methods where different Runge-Kutta tableaux are used for the p and...
متن کاملEmbedded explicit Runge-Kutta type methods for directly solving special third order differential equations y'''=f(x, y)
In this paper three pairs of embedded Runge–Kutta type methods for directly solving special third order ordinary differential equations (ODEs) of the form denoted as RKD methods are presented. The first is the RKD4(3) pair which is third order embedded in fourth-order method has the property first same as last (FSAL) whereby the last row of the coefficient matrix is equal to the vector output. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Computers & Mathematics with Applications
دوره 62 شماره
صفحات -
تاریخ انتشار 2011