Application of the Haar wavelet approach for solving stiff differential equations is discussed. Solution of singular perturbation problems is also considered. Efficiency of the recommended method is demonstrated by means of four numerical examples, mostly taken from well-known textbooks.

A component-based methodology to derive parallel stiff Ordinary Differential Equation (ODE) solvers for multicomputers is presented. The methodology allows the exploitation of the multilevel parallelism of this kind of numerical algorithms and the particular structure of ODE systems by using parallel linear algebra modules. The approach furthers the reusability of the design specifications and ...

Stabilized or Chebyshev explicit methods have been widely used in the past to solve stiff ordinary differential equations. Making use of special properties of Chebyshev-like polynomials, these methods have favorable stability properties compared to standard explicit methods while remaining explicit. A new class of such methods, called ROCK, introduced in [Numer. Math., 90, 1-18, 2001] has recen...

Recently developed physics-informed neural network (PINN) has achieved success in many science and engineering disciplines by encoding physics laws into the loss functions of network, such that not only conforms to measurements, initial boundary conditions but also satisfies governing equations. This work first investigates performance PINN solving stiff chemical kinetic problems with equations...

A semi-implicit formulation of the method of spectral deferred corrections (SISDC) for ordinary differential equations with both stiff and non-stiff terms is presented. Several modifications and variations to the original spectral deferred corrections method by Dutt, Greengard, and Rokhlin concerning the choice of integration points and the form of the correction iteration are presented. The st...

A novel and efficient technique is developed for estimating the local error per step when firstand second-order accurate projective integrators are applied to stiff multiscale systems. The estimation can be done on-the-fly; that is, the accumulated local error is readily estimated at the end and during the course of computing the solution at each outer time step. We demonstrate the effectivenes...

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...

Implicit-explicit (IMEX) Runge-Kutta methods play a major rule in the numerical treatment of differential systems governed by stiff and non-stiff terms. This paper discusses order conditions and symplecticity properties of a class of IMEX Runge–Kutta methods in the context of optimal control problems. The analysis of the schemes is based on the continuous optimality system. Using suitable trans...

Abstract In this work, we study the A [ ? ] – stability of additive methods Runge- Kutta kind orders ranging from 2 up to 4 that will be applied for determining some stiff nonlinear system ODEs. Moreover, find function Runge-Kutta method and type order 2,3, 4. Where ( A,B 1 ) is A-stable semi-implicit explicit. Furthermore, term managed by while no treated explicit Runge method. Those are suita...