Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

Numerical Methods for Ordinary Differential Equations

Mixed mode tensile – In plane shear fracture energy determination for hot mix asphalt mixtures under intermediate temperature conditions

In this paper, an attractive reliable analytical technique is implemented for constructing numerical solutions for the fractional Lienard’s model enclosed with suitable nonhomogeneous initial condi...

https://www.worldscientific.com/doi/pdf/10.1142/S0218348X20400071

Piecewise optimal fractional reproducing kernel solution and convergence analysis for the atangana–baleanu–caputo model of the lienard’s equation

The aim of this paper is to propose the Atangana–Baleanu fractional methodology for fathoming the Van der Pol damping model by using the reproducing kernel algorithm. To this end, we discuss the ma...

https://www.worldscientific.com/doi/pdf/10.1142/S0218348X20400101

The Reproducing Kernel Algorithm for Numerical Solution of Van Der Pol Damping Model in View of the Atangana-Baleanu Fractional Approach

Evaluation of the effects of anti-stripping agents on the performance of asphalt mixtures

General Linear Methods (GLMs) were introduced as the natural generalizations of the classical Runge---Kutta and linear multistep methods. An extension of GLMs, so-called SGLMs (GLM with second derivative), was introduced to the case in which second derivatives, as well as first derivatives, can be calculated. In this paper, we introduce the definitions of consistency, stability and convergence for an SGLM. It will be shown that in SGLMs, stability and consistency together are equivalent to convergence. Also, by introducing a subclass of SGLMs, we construct methods of this subclass up to the maximal order which possess Runge---Kutta stability property and A-stability for implicit ones.

Ali Abdi

Papers

Evaluation of the effects of anti-stripping agents on the performance of asphalt mixtures

An extension of general linear methods

Maximal order for second derivative general linear methods with Runge-Kutta stability

Implementation of Nordsieck second derivative methods for stiff ODEs

On the construction of second derivative diagonally implicit multistage integration methods for ODEs