A review of diagonally implicit Runge-Kutta (DIRK) methods applied to rst-order ordinary di
erential equations (ODEs) is undertaken. The goal of this review is to summarize the …

Modified Runge–Kutta (mRK) methods can have interesting properties as their coefficients
may depend on the step length. By a simple perturbation of very few coefficients we may …

An effectively four-stage, sixth-order, hybrid explicit Numerov-type method is presented for
the solution of the special second-order initial value problem. The new method uses variable …

Runge‐Kutta pairs sharing orders 5 and 4 are among the most celebrated methods for
solving initial value problems. Here, after considering the phase lag as a function of …

Abstract Two new Runge–Kutta (RK) pairs of orders 6 (4) and 7 (5) are presented for solving
numerically the inhomogeneous linear initial value problems with constant coefficients …

A purely interpolatory approach is applied for derivation of methods mentioned in the title.
Four parameters remain free and are enough for presenting a method with minimal …

A two–stage, explicit, hybrid four–step method of sixth order for the solution of the special
second order initial value problem is presented here. The new method is trigonometric fitted …

High algebraic order Runge–Kutta embedded methods are commonly used when stringent
tolerances are demanded. Traditionally, various criteria are satisfied while constructing …

We consider the mildly stiff and stiff inhomogeneous linear initial value Problems sharing
constant coefficients. Exponential Runge–Kutta methods are considered to tackle this …

Runge‐Kutta (RK) pairs sharing orders 6 and 5 are widely used for solving initial value
problems. Thus, we consider the dispersion from a standard cyclic orbit as a function of …