Over the last few years there has been a growing and renovated interest in the numerical study of Random Differential Equations (RDEs). On one hand it is motivated by the fact that RDEs have played an important role in the ...

We propose a new numerical method for the computer simulation of the semi-linear transport equation. Based on the stochastic characteristic method and the Local Linearization technique, we construct an effi cient and stable ...

Periodic waves are investigated in a system composed of a Kuramoto-Sivashinsky-Korteweg-de Vries (KS-KdV) equation linearly coupled to an extra linear dissipative one. The model describes, e.g., a two-layer liquid film ...

Periodic waves are investigated in a system composed of a Kuramoto-Sivashinsky-Korteweg-de Vries (KS-KdV) equation linearly coupled to an extra linear dissipative one. The model describes, e.g., a two-layer liquid film ...

A new approach for the construction of high order A-stable explicit integrators for ordinary differential equations (ODEs) is theoretically studied. Basically, the integrators are obtained by splitting, at each time step, ...

We show numerically that the one-dimensional quintic complex Ginzburg-Landau equation admits four different types of stable hole solutions. We present a simple analytic method which permits to calculate the region of ...