The purpose of this paper is to construct methods for solving stiff ODEs, in particular singular perturbation problems. We consider embedded pairs of singly diagonally implicit Runge-Kutta methods with an explicit first stage (ESDIRKs). Stiffly accurate pairs of order 3/2, 4/3 and 5/4 are constructed. AMS Subject Classification: 65L05

This paper studied the 2–point improved block backward differentiation formula for solving stiff initial value problems proposed by Musa et al (2013) and further established the necessary conditions for the convergence of the method. It is shown that the method is both zero stable and consistent. The order of the method is also derived.

In this paper, a new difference scheme based on C1-quintic splines is derived for the numerical solution of the stiff delay differential equations. Convergence results shows that the methods have a convergence of order five. Moreover, the stability analysis properties of these methods have been studied. Finally, numerical results illustrating the behavior of the methods when faced with some dif...

This paper presents new fifth-order diagonally implicit Runge-Kutta integration formulas for stiff initial value problems, designed to be Lstable method. The stability of the method is analyzed and numerical results are shown to verify the conclusions. Mathematics Subject Classifications: 51N20, 62J05, 70F99

We consider inital-value problems governed by a system of autonomous ordinary differential equations (ODEs). When the required integration stepsize of the ODE system is very very small in comparison to the time domain of interest. Then the initial-value problem is said to be stiff.

Inspired by the ubiquity of composite filamentous networks in nature, we investigate models of biopolymer networks that consist of interconnected floppy and stiff filaments. Numerical simulations carried out in three dimensions allow us to explore the microscopic partitioning of stresses and strains between the stiff and floppy fractions cs and cf and reveal a nontrivial relationship between th...

Many important differential equations model quantities whose value must remain positive or stay in some bounded interval. These bounds may not be preserved when the is solved numerically. We propose to ensure positivity other by applying Runge-Kutta integration which method weights are adapted order enforce bounds. The chosen at each step after calculating stage derivatives, a way that also pre...

We present two families of explicit and implicit BDF formulas, capable of the exact integration (with only round-off errors) of differential equations which solutions belong to the space generated by the linear combinations of exponential of matrices, products of the exponentials by polynomials and products of those matrices by ordinary polynomials. Those methods are suitable for stiff and high...

Explicit methods have previously been proposed for parabolic PDEs and for stiff ODEs with widely separated time constants. We discuss ways in which Differential Algebraic Equations (DAEs) might be regularized so that they can be efficiently integrated by explicit methods. The effectiveness of this approach is illustrated for some simple index three problems. AMS subject classification (2000): 6...