Stabilized Integrating Factor Runge--Kutta Method and Unconditional Preservation of Maximum Bound Principle

Explicit Stabilized Runge-Kutta Methods

Runge-Kutta-Chebyshev projection method

In this paper a fully explicit, stabilized projection method called the Runge-Kutta-Chebyshev (RKC) Projection method is presented for the solution of incompressible Navier-Stokes systems. This method preserves the extended stability property of the RKC method for solving ODEs, and it requires only one projection per step. An additional projection on the time derivative of the velocity is perfo...

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...

Runge – Kutta – Chebyshev projection method q

In this paper a fully explicit, stabilized projection method called the Runge–Kutta–Chebyshev (RKC) projection method is presented for the solution of incompressible Navier–Stokes systems. This method preserves the extended stability property of the RKC method for solving ODEs, and it requires only one projection per step. An additional projection on the time derivative of the velocity is perfo...

A quasi-randomized Runge-Kutta method

We analyze a quasi-Monte Carlo method to solve the initial-value problem for a system of differential equations y′(t) = f(t, y(t)). The function f is smooth in y and we suppose that f and D1 yf are of bounded variation in t and that D2 yf is bounded in a neighborhood of the graph of the solution. The method is akin to the second order Heun method of the Runge-Kutta family. It uses a quasi-Monte...