Solving Linear Boundary Value Problems Via Non-commutative Gröbner Bases

Solving Linear Boundary Value Problems via Non-commutative Gröbner Bases

A new approach for symbolically solving linear boundary value problems is presented. Rather than using general-purpose tools for obtaining parametrized solutions of the underlying ODE and fitting them against the specified boundary conditions (which may be quite expensive), the problem is interpreted as an operator inversion problem in a suitable Banach space setting. Using the concept of the o...

Solving the non linear system of third order boundary value problems by using He's homotopy perturbation method

Solving thousand-digit Frobenius problems using Gröbner bases

A Gröbner basis-based algorithm for solving the Frobenius Instance Problem is presented, and this leads to an algorithm for solving the Frobenius Problem that can handle numbers with thousands of digits. Connections to irreducible decompositions and Hilbert functions are also presented.

B-Spline Finite Element Method for Solving Linear System of Second-Order Boundary Value Problems

In this paper, we solve a linear system of second-order boundary value problems by using the quadratic B-spline nite el- ement method (FEM). The performance of the method is tested on one model problem. Comparisons are made with both the analyti- cal solution and some recent results.The obtained numerical results show that the method is ecient.

SOLVING LINEAR SIXTH-ORDER BOUNDARY VALUE PROBLEMS BY USING HYPERBOLIC UNIFORM SPLINE METHOD

In this paper, a numerical method is developed for solving a linear sixth order boundaryvalue problem (6VBP ) by using the hyperbolic uniform spline of order 3 (lower order). Thereis proved to be first-order convergent. Numerical results confirm the order of convergencepredicted by the analysis.