The problem of the region of stability of the fourth order-Runge-Kutta method for the solution of systems of differential equations is studied. This region can be characterized by means of linear ...

Finite element methods provide a robust, mature family of discretizations for partial differential equations, as they provide rigorous theory, general geometry, and fast solvers. Modern trends in ...

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"- I want to implement and illustrate the [Runge-Kutta method](https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods) (actually, different variants), in the ...

Abstract: An explicit Runge-Kutta (RK) method with an extended stability region (ESR) can be constructed based on an RK method with a stability function corresponding to the Taylor series for the ...

Abstract: Ordinary differential equations are solved numerically using number of methods. In this paper, an analysis of finding out the solution of n-th order differential equations has been done ...

ABSTRACT: In this paper, we propose two new explicit Almost Runge-Kutta (ARK) methods, ARK3 (a three stage third order method, i.e., s = p = 3) and ARK34 (a four-stage third-order method, i.e., s = 4, ...

ABSTRACT: In this paper, the Ito-Taylor expansion of stochastic differential equation is briefly introduced. The colored rooted tree theory is applied to derive strong order 1.0 implicit stochastic ...