granular media of CoCrPtTa structure (type a) and micromagnetic standard problem #4 has been done. Moreover, an investigation of the effect of the maximum dimension of the Krylov subspace projection methods, within the Ordinary Differential Equations (ODEs) context, on the speed of micromagnetic simulations on granular media of Co structure (type b) has been done. The stiffness of the problems ...

In this paper we introduce a low cost method for integrating large dimensional linear initial value problems based on the Arnoldi algorithm for matrix functions. We also describe a very efficient step-size control technique and compare a resulting algorithm of order 4 with the standard Matlab solvers on linear stiff problems arising from the discretization of parabolic equations.

Abstract In recent years, physics-informed neural networks (PINN) have been used to solve stiff-PDEs mostly in the 1D and 2D spatial domain. PINNs still experience issues solving 3D problems, especially, problems with conflicting boundary conditions at adjacent edges corners. These discontinuous solutions corners that are difficult learn for a continuous activation function. this review paper, ...

This paper describes the development of a four-point fully implicit block method for solving first order ordinary differential equations (ODEs) using variable step size. This method will estimate the solutions of initial value problems (IVPs) at four points simultaneously. The method developed is suitable for the numerical integration of non-stiff and mildly stiff differential systems. The perf...

3 Discrete stochastic models are widely used to describe current engineer4 ing and logistics problems. The stochastic simulation of such models can get 5 very expensive if the models are stiff or rare system events are of interest. 6 Proxels are a state space-based simulation technique that does not have these 7 drawbacks. They implicitly use a discrete-time Markov chain to determin8 istically ...

In this paper, new integration methods for stiff ordinary differential equations (ODEs) are developed. Following the idea of quantization–based integration (QBI), i.e., replacing the time discretization by state quantization, the proposed algorithms generalize the idea of linearly implicit algorithms. Also, the implementation of the new algorithms in a DEVS simulation tool is discussed. The eff...

Linear multistep methods using higher derivatives are discussed. The order of damping at infinity which measures the stability behavior of a fc-step method for large h is introduced. ,4-stable methods with positive damping order are most suitable for stiff problems. A method for computing the damping order is given. Necessary and sufficient conditions for A -stability, A (a) -stability and stif...

R n , parameters A aij R s , c b R , 1l : 1 1 T and step size hm. F denotes the straightforward extension of f to R . Here, denotes the Kronecker tensor product. Notice that the EPTRK method 2 requires only one sequential function evaluation per step on a parallel computer with s processing elements. Numerical experiments with a variable step size implementation on a shared memory computer have...

In this paper, we consider the development of an extended block integrator for the solution of stiff and oscillatory first-order Ordinary Differential Equations (ODEs) using interpolation and collocation techniques. The integrator was developed by collocation and interpolation of the combination of power series and exponential function to generate a continuous implicit Linear Multistep Method (...