Bounds for solutions of systems of linear equations

Exact and numerical solutions of linear and non-linear systems of fractional partial differential equations

The present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. The proposed scheme is based on Laplace transform and new homotopy perturbation methods. The fractional derivatives are considered in Caputo sense. To illustrate the ability and reliability of the method some examples are provided. The results ob...

Bounds on Positive Integral Solutions of Linear Diophantine Equations

Assuming the existence of a solution, we find bounds for small solutions x of the finite matrix equation Ax = B, where each entry of A, B is an integer, and x is a nontrivial column vector with nonnegative integer entries. 0. Introduction. In [1], [5] and [6] there arise in a topological setting, systems of linear equations with integer coefficients. The problem is to find a bound K depending o...

exact and numerical solutions of linear and non-linear systems of fractional partial differential equations

the present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. the proposed scheme is based on laplace transform and new homotopy perturbation methods. the fractional derivatives are considered in caputo sense. to illustrate the ability and reliability of the method some examples are provided. the results ob...

Least Squares Solutions of Inconsistent Fuzzy Linear Matrix Equations

Bounds for Solutions of Ordinary Differential Equations

1. An upper bound for the norm of a system of ordinary differential equations can be obtained by comparison with a related first order differential equation, [4; 8]. This first order equation depends on an upper bound for the norm of the right side of the system. Recently, it has been pointed out [l; 6] that this same upper bound also gives a lower bound for the norm of the solution in terms of...