Third-order Composite Runge Kutta Method for Solving Fuzzy Differential Equations

Solving Hybrid Fuzzy Fractional Differential Equations by Runge Kutta 4th Order Method

In this paper we study numerical methods for hybrid fuzzy fractional differential equation, Degree of Sub element hood and the iteration method is used to solve the hybrid fuzzy fractional differential equations with a fuzzy initial condition.

Numerical solution of first-order fully fuzzy differential equations by Runge-Kutta Fehlberg method under strongly generalized H-differentiability

In this paper we propose Runge-Kutta Fehlberg method for solving fully fuzzy differential equations (FFDEs) of the form y ′ (t) = a⊗ y(t), y(0) = y0, t ∈ [0,T ] under strongly generalized H-differentiability. The algorithm used here is based on cross product of two fuzzy numbers. Using cross product we investigate the problem of finding a numerical approximation of solutions. The convergence of...

Nonstandard explicit third-order Runge-Kutta method with positivity property

When one solves differential equations, modeling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. Based on general theory for positivity, with an explicit third-order Runge-Kutta method (we will refer to it as RK3 method) pos...

Embedded explicit Runge – Kutta type methods for directly solving special third order differential equations

Zero-Dissipative Explicit Runge-Kutta Method for Periodic Initial Value Problems

Abstract—In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing ...