Galerkin approximations for initial value problems with known end time conditions

Diagonal Pad ] Approximations for Initial Value Problems *

Diagonal Padd approximations to the time evolution operator for initial value problems are applied in a novel way to the numerical solution of these problems by explicitly factoring the polynomials of the approximation. A remarkable gain over conventional methods in efficiency and accuracy of solution is obtained.

One-Step Piecewise Polynomial Galerkin Methods for Initial Value Problems*

A new approach to the numerical solution of systems of first-order ordinary differential equations is given by finding local Galerkin approximations on each subinterval of a given mesh of size h. One step at a time, a piecewise polynomial, of degree n and class C°, is constructed, which yields an approximation of order 0(A*") at the mesh points and 0(A"+1) between mesh points. In addition, the ...

Galerkin Approximations of Abstract Parabolic Boundary Value Problems

Galerkin approximations of an abstract parabolic boundary value problem with "rough" boundary data are considered. The optimal rates of convergence in Lp[0T; L2(ti)] norms for L [07"; L2(T)] boundary terms are derived.

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation

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.