In this paper, a novel, simple yet efficient method is proposed to approximately solve linear ordinary differential equations (ODEs). Emphasis is put on second-order linear ODEs with variable coefficients. First, the ODE to be solved is transformed to either a Volterra integral equation or a...

This work investigates the inverse problem of reconstructing a spacewise dependent heat source in the parabolic heat equation using a final temperature measurement. Such problem has important application in a large field of applied science. On the basis of the optimal control framework, the...

We examine the effects of discreteness on a prototypical example of a collapse exhibiting partial differential equation (PDE). As our benchmark example, we select the discrete nonlinear Schrödinger (DNLS) equation. We provide a number of physical settings where issues of the interplay of...

The paper is concerned with the numerical solution of non-linear conservation laws, and the contribution biomechanical models of spine and of loaded wrist are formulated and analysed. The models are based on a contact problem in non-linear elastic rheology. The stress–strain relation is...

The point of this paper is to review recent theoretical and experimental results related to scalability of the FETI based domain decomposition algorithm that was proposed recently by Dostál, Friedlander, Santos and Gomes for numerical solution of discretized variational inequalities. After...

In the paper, the quasi-coupled semi-coercive contact problem in thermo-elasticity is investigated. The FEM analysis of the problem is also presented.

The main goal of this work is to give an adequate method permitting the resolution of a bilateral obstacle problem, by introducing a convex continuous mapping which subdifferential characterizes the sets of noncontact with the obstacles, then solving a Dirichlet problem to get the solution of...

This paper considers the optimal consumption and investiment policy for an investor who has available one bank account paying a fixed interest rate r and n risky assets whose prices are log-normal diffusions. We suppose that transactions between the assets incur a cost proportional to the size...