A stability analysis of the Borel–Padé–Laplace series summation technique, used as explicit time integrator, is carried out. Its numerical performance on stiff and non-stiff problems analyzed. Applications to ordinary partial differential equations are presented. The results compared with those many popular schemes designed for equations.

A new BDF-type scheme is proposed for the numerical integration of the system of ordinary differential equations that arises in the Method of Lines solution of time-dependent partial differential equations. This system is usually stiff, so it is desirable for the numerical method to solve it to have good properties concerning stability. The method proposed in this article is almost L-stable and...

Stiff delay differential equations are frequently utilized in practice, but their numerical simulations difficult due to the complicated interaction between stiff and terms. At moment, only a few low-order algorithms offer acceptable convergent stable features. Exponential integrators type of efficient approach for problems that can eliminate influence stiffness on scheme by precisely dealing w...

Stabilized Runge–Kutta methods are especially efficient for the numerical solution of large systems stiff nonlinear differential equations because they fully explicit. For semi-discrete parabolic problems, instance, stabilized overcome stringent stability condition standard without sacrificing explicitness. However, when stiffness is only induced by a few components, as in presence spatially lo...

It is well known that the numerical solution of stiff stochastic ordinary differential equations leads to a step size reduction when explicit methods are used. This has led to a plethora of implicit or semi-implicit methods with a wide variety of stability properties. However, for stiff stochastic problems in which the eigenvalues of a drift term lie near the negative real axis, such as those a...

A model is presented for stability for an extension of linear multistep methods for stiff ordinary differential equations. The method is based on a prediction followed by a fixed number of corrections obtained by a Newton scheme with inexact Jacobian matrix. The impact on stability of error in the matrix over a broad range of linear, constant coefficient equations is modeled. The model provides...

Multiscale differential equations arise in the modeling of many important problems in the science and engineering. Numerical solvers for such problems have been extensively studied in the deterministic case. Here, we discuss numerical methods for (mean-square stable) stiff stochastic differential equations. Standard explicit methods, as for example the EulerMaruyama method, face severe stepsize...