Comparison of Numerical Methods for SWW Equations

The Comparison of Numerical Methods for Solving Polynomial Equations

In this paper we compare the Turan process [5]-[6] with the Lehmer-Schur method [2]. We prove that the latter is better. 1. The Algorithms. We first describe the Turan process [5]-[6] which can be considered as an improvement of Graeffe's method. For the complex polynomial (1.1) P0(z)=t «/o*' = ° (fl/o G C, a00an0 * 0), 7=0 the method can be formulated as follows. Let (1.2) Pj(z) = Phx(sfz~)phx...

Numerical methods for Lyapunov equations

This chapter is about numerical methods for a particular type of equation expressed as a matrix equality. The Lyapunov equation is the most common problem in the class of problems called matrix equations. Other examples of matrix equations: Sylvester equation, Stein equation, Riccati equation. Definition 4.0.1. Consider two square matrices A, W ∈ Rn×n. The problem to find a square matrix X ∈ Rn...

Numerical Methods for Differential Equations

Numerical Methods for Differential Equations

After revisiting some practical problems of numerical methods by playing with models introduced in Chapter 2, we will investigate the two most important properties of numerical algorithms—stability and accuracy. This is done most easily in the context of the simplest numerical method, i.e., the explicit Euler method (Section 5.2). The problem of solving stiff differential equations is addressed...

Numerical Methods for Ultraparabolic Equations

We analyze semidiscrete and fully discrete finite element approximations to the solution of an initial boundary value problem for a model ultraparabolic equation.