A numerical algorithm for solving stiff boundary value problems with turning points is presented. The stiff systems are characterized as singularly perturbed differential equations. The numerical method is derived by appropriately discretizing the boundary layer and connection theory for such systems. Numerical results demonstrate the effectiveness of the method. In many cases the calculation p...

In this publication, we consider IMEX methods applied to singularly perturbed ordinary differential equations. We introduce a new splitting into stiff and non-stiff parts that has a direct extension to systems of conservation laws, and investigate analytically and numerically its performance. We show that this splitting can in some cases improve the order of convergence, showing that the phenom...

An implicit numerical integration algorithm based on generalized coordinate partitioning is presented for the numerical solution of differential–algebraic equations of motion arising in multibody dynamics. The algorithm employs implicit numerical integration formulas to express independent generalized coordinates and their first time derivative as functions of independent accelerations at discr...

Currently there are two general ways to solve stiff differential equations numerically. The first approach is based on implicit methods and the second uses explicit stabilized Runge–Kutta methods, also known as Chebyshev methods. Implicit methods are great for very stiff problems of not very large dimension, while stabilized explicit methods are efficient for very big systems of not very large ...

This paper introduces two new numerical methods for integration of stiff ordinary differential equations. Following the idea of quantization based integration, i.e., replacing the time discretization by state quantization, the new methods perform first and second order backward approximations allowing to simulate stiff systems. It is shown that the new algorithms satisfy the same theoretical pr...

In this paper, a nonlinear stiff differential equation is solved by using the Rosenbrock iterative method, modified homotpy analysis method and power series method. The approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relations. Some numerical examples are studied to demonstrate the accuracy of the presented meth...

This paper is concerned with time-stepping numerical methods for computing stiff semi-discrete systems of ordinary differential equations for transient hypersonic flows with thermo-chemical nonequilibrium. The stiffness of the equations is mainly caused by the viscous flux terms across the boundary layers and by the source terms modeling finite-rate thermo-chemical processes. Implicit methods a...

Validated Numerical Bounds on the Global Error for Initial Value Problems for Stiff Ordinary Differential Equations Chao Yu Master of Science Graduate Department of Computer Science University of Toronto 2004 There are many standard numerical methods for initial value problems (IVPs) for ordinary differential equations (ODEs). Compared with these methods, validated methods for IVPs for ODEs pro...

Unconditionally stable implicit time-marching methods are powerful in solving stiff differential equations efficiently. In this work, a novel framework to handle physical terms implicitly is proposed. Both and numerical stiffness originating from convection, diffusion source (typically related reaction) can be handled by set of predefined Time-Accurate highly-Stable Explicit (TASE) operators un...