Numerical Solution of Reaction–Diffusion Equations with Convergence Analysis

Convergence Analysis of Projection Methods for the Numerical Solution of Large Lyapunov Equations

The numerical solution of large-scale continuous-time Lyapunov matrix equations is of great importance in many application areas. Assuming that the coefficient matrix is positive definite, but not necessarily symmetric, in this paper we analyze the convergence of projection type methods for approximating the solution matrix. Under suitable hypotheses on the coefficient matrix, we provide new as...

Numerical Solution of Nonlinear Differential Equations with Algebraic Constraints I: Convergence Results for Backward Differentiation Formulas

In this paper we investigate the behavior of numerical ODE methods for the solution of systems of differential equations coupled with algebraic constraints. Systems of this form arise frequently in the modelling of problems from physics and engineering; we study some particular examples from electrical networks, fluid dynamics and constrained mechanical systems. We show that backward differenti...

Numerical Solution of Fuzzy Linear Volterra Integral Equations of the Second Kind by Homotopy Analysis Method

Numerical Solution of Differential Equations

Error analysis of the numerical solution of split differential equations

The operator splitting method is a widely used approach for solving partial differential equations describing physical processes. Its application usually requires the use of certain numerical methods in order to solve the different split sub-problems. The error-analysis of such a numerical approach is a complex task. In the present paper we show that an interaction error appears in the numerica...