Runge-Kutta
Numerical stability and oscillation of the Runge Kutta methods for the differential equations with piecewise continuous arguments alternately of retarded and advanced type
... stability region of Runge-Kutta methods is determined. The conditions that the analytic stability region is contained in the numerical stability region are obtained. A necessary and sufficient condition for ...
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A third order Runge-Kutta method based on a convex combination of Lehmer means
... order Runge-Kutta (RK3) method are the RK3 method based on the harmonic mean [12], the RK3 method based on geometry mean [6], the RK3 method based on the contraharmonic mean [1], and RK3 methods based on a ...
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Performance Analysis and Maintenance Scheduling of a System using Runge-Kutta Method
... The paper describes the availability of butter production system in a milk industry. This system consists of six subsystems namely filter, chiller, separator, pasteurizer, churner and packing. Availability has been ...
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Difference schemes for nonlinear BVPs using Runge Kutta IVP solvers
... The aim of this paper is to remove these two drawbacks and, therefore, to improve the computational complexity and the effectiveness of TDS for problem (1.1). We pro- pose a new implementation of TDS with the following ...
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Stepsize Selection in Explicit Runge Kutta Methods for Moderately Stiff Problems
... Stiff initial-value problems (IVPs) are often solved nu- merically using implicit A-stable Runge-Kutta (RK) me- thods. In such methods, there is no need to adjust the stepsize for the sake of stability, ...
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High Order Explicit Two-Step Runge-Kutta Methods for Parallel Computers
... In this paper we study a class of explicit pseudo two-step Runge-Kutta methods ( EPTRK methods ) with additional.. weights v.[r] ...
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Implicit Runge-Kutta Method for Van Der Pol Problem
... Abstract: In this manuscript the implicit Runge-Kutta (IRK) method, with three slopes of order five has been explained, and is applied to Van der pol stiff differential equation. Truncation error, of order ...
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Stochastic Runge-Kutta method for stochastic delay differential equations
... stochastic Runge–Kutta with time delay, we propose to derive SRK for SDDE in this research as well as to approximate the strong solution of SDDE via this ...
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Asymptotical stability of Runge Kutta for a class of impulsive differential equations
... The paper is organized as follows. In Section , we obtain the existence, uniqueness, and asymptotical stability of the exact solutions of (.). In Section , we study the asymptotical stability of the ...
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Transient Analysis Of Electrical Circuits Using Runge-Kutta Method
... Generally, the project named Transient Analysis of Electrical Circuit using Runge- Kutta method utilizes many resources from previous works of researchers. In this chapter, there are three major parts which ...
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Convergence of an Exponential Runge–Kutta Method for Non-smooth Initial Data
... Theorem 1. Assume that problem (1) fulfill the hypotheses of Lemma 2 given in Gondal [5] and that AB = BA. For the numerical solution, we consider the exponential Runge- Kutta method (6). Also suppose that ...
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Numerical accuracy between Runge-Kutta Fehlberg method and Adams-Bashforth method for first order ordinary differential equations with boundary value
... is Runge-Kutta fehlberg method, and thedouble step method that is the Adams- Bashforth method in solving an ordinary differential equation of first order and second ...the Runge-Kutta fehlberg ...
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Nonstandard explicit third-order Runge-Kutta method with positivity property
... where ∆x and ∆y being the mesh width in the x-direction and y-direction, respectively. For more details see [6, p. 307]. In Figure 3, some numerical results have been shown on a 50×50 grid for the classical fourth-order ...
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Runge Kutta residual distribution schemes
... Abstract We are concerned with the solution of time-dependent non-linear hyperbolic par- tial differential equations. We investigate the combination of residual distribution methods with a consistent mass matrix ...
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Two Implicit Runge Kutta Methods for Stochastic Differential Equation
... Recently, many scholars have successfully derived some methods for SDEs for both Itô and Stratonovich forms. Burrage and Burrage [1-3] established the colored rooted tree theory and Stochastic B-series expansion. Tian ...
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Preconditioning of implicit Runge-Kutta methods
... 1. Introduction. We consider the numerical solution of implicit systems of differential equations by fully implicit Runge-Kutta (IRK) methods. A major problem in obtaining an efficient implementation of IRK ...
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A New 4th Order Hybrid Runge-Kutta Methods for Solving Initial Value Problems (IVPs)
... derivative method using the usual arithmetic mean respectively. Akanbi [5] developed a third-order method based on the geometric mean. But [6] and [7] introduced the concept of the heronian mean Evans and Yaacob [8] ...
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The comparison of runge kutta and adams bashforh moulton methods for the first order ordinary differential equations
... = 4 which is a spiral curve (Davis, 1962 as cited in Hull et al., 1972). As it is shown above the problems selected have exact solutions. This is helpful to compare the approximated values with the exact values and to ...
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On the Derivation and Implementation of a Four Stage Harmonic Explicit Runge Kutta Method*
... In previous papers [1] and [2], the authors presented a three stage method based on the harmonic mean and a multi-derivative method using the usual arithmetic mean respectively. Akanbi [3] developed a third-order me- ...
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Numerical Solution of First Order Linear Differential Equations in Fuzzy Environment by Modified Runge-Kutta- Method and Runga- Kutta-Merson-Method under generalized H-differentiability and its Application in Industry
... Modified Runge Kutta Method and Runge Kutta Mersion method was taken into account to estimate the solution of first order linear ordinary differential equation with fuzzy initial condition, ...
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