Initial value method for general singular perturbation problems

Differential Quadrature Method for the General Singular Perturbation Problems

This paper extends the application of Differential Quadrature Method (DQM) for finding the numerical solution of general singularly perturbed two point boundary value problems with a boundary layer at right end point or both end point or at an internal point. The Differential Quadrature Method is an efficient descritization technique in solving initial and /or boundary value problems accurately...

Laplace Decomposition Method for Solving Singular Initial Value Problems

In this paper, Laplace Decomposition Method (LDM) which is coupling of Laplace Transform (LT) and Adomian’s Decomposition Method (ADM) is employed to construct the exact solution of two mathematical problems which arises in diverse fields of physics. It has been observed that this proposed coupling is very efficient and reliable for the solution of the nonlinear problems. Numerical results and ...

MODIFIED K-STEP METHOD FOR SOLVING FUZZY INITIAL VALUE PROBLEMS

We are concerned with the development of a K−step method for the numerical solution of fuzzy initial value problems. Convergence and stability of the method are also proved in detail. Moreover, a specific method of order 4 is found. The numerical results show that the proposed fourth order method is efficient for solving fuzzy differential equations.

Acceleration Techniques for Singular Initial Value Problems

The acceleration technique known as Iterated Defect Correction (IDeC) for the numerical solution of singular initial value problems is investigated. IDeC based on the implicit Euler method performs satisfactorily and can thus be used for the eÆcient solution of singular boundary value problems with the shooting method. Higher order one-step methods like the box scheme or the trapezoidal rule ca...

On the Convergence of Continuous-Time Waveform Relaxation Methods for Singular Perturbation Initial Value Problems