An initial value method for orthogonal polynomials

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.

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...

Variational Iteration Method for Initial and Boundary Value Problems Using He's Polynomials

This paper outlines a detailed study of the coupling of He’s polynomials with correction functional of variational iteration method VIM for solving various initial and boundary value problems. The elegant coupling gives rise to the modified versions of VIM which is very efficient in solving nonlinear problems of diversified nature. It is observed that the variational iteration method using He’s...

Optimal Stability Polynomials for Numerical Integration of Initial Value Problems

- - - - - o ' " A STANDARD METHOD FOR SURFACE FITTING BY ORTHOGONAL POLYNOMIALS

An algorithm for least squares fitting of a polynomial to a function z(x.y) of two independent variables is described. It is assumed that the function is given by a number of "measured values". which may be arbitrarily distributed over the ~Yplane. The polynomial is constructed as a linear combination of a set of polynomials which are orthonormalized over the set of given data points by the mod...