the spline collocation method  is employed to solve a system of linear and nonlinear fredholm and volterra integro-differential equations. the solutions are collocated by cubic b-spline and the integrand is approximated by the newton-cotes formula. we obtain the unique solution for linear and nonlinear system $(nn+3n)times(nn+3n)$ of integro-differential equations. this approximation reduces th...

After discretisation of the partial differential equations from mechanics one usually obtains large systems of (non)linear equations. Their efficient solution requires the use of fast iterative methods. Multi-grid iterations are able to solve linear and nonlinear systems with a rather fast rate of convergence, provided the problem is of elliptic type. The contribution describes the basic constr...

We prove the generalized Hyers--Ulam stability  of $n$-th order linear differential equation of the form $$y^{(n)}+p_{1}(x)y^{(n-1)}+ cdots+p_{n-1}(x)y^{prime}+p_{n}(x)y=f(x),$$ with condition that there exists a non--zero solution of corresponding homogeneous equation. Our main results extend and improve the corresponding results obtained by many authors.

For the detection of contaminations in urban water supply networks we introduce a continuous optimal control model governed by partial differential equations. We derive a linear mixedinteger model by discretization of the dynamics of the partial differential equations and by approximations to the cost functional. Finally, we present numerical results for artificial and real-world networks.