A New Numerical Method for Solving Stiff Initial Value Problems

An automatic multistep method for solving stiff initial value problems

A multistep method with matricial coefficients is developed. It can be used to solve stiff initial value problems of the form y’= Ay + g(x,y). This method bears the nature of the classical Adams-Bashforth-Moulton PC formula and can be shown to be consistent, convergent and A-stable. A careful reformulation of this method legitimatizes the implementation of this algorithm in a variable-step vari...

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.

A New Iterative Method for Solving Initial Value Problems

In this paper, we introduce a new parameter iteration method (P-Iteration for short) ,which can be applied on Adams-Moulton methods to solve initial value problems. Compared with Jacobi iteration method, it has three advantages: (1) it may significantly implement the stable region of the iterative process such that we can efficiently use the large stable region of implicit formula; (2) it allow...

A new numerical method by revised measure theory for solving the nonlinear initial value problems

In this paper, we introduce a new technique to find the approximate solution of a nonlinear initial value problem (IVP). By introducing an artificial zero cost function and a linear functional, the problem is modified into one consisting of the minimization of a positive linear functional over a set of Radon measures. Then we obtain an optimal measure which is approximated by a finite combinati...

A new variable step size block backward differentiation formula for solving stiff initial value problems