Semi-implicit discretization of abstract evolution equations

Rok, strany: 1994, 207 - 212

Abstract evolution equations in an arbitrary Banach space $X$, like $\dot u=f(t, u, u)$, $t\in (0, T]$, subject to the initial value $u(0)= u₀$, are discretized by a semi-implicit version of the Euler method. The basic assumptions being that $f(t, ·, v)$ is one-sided Lipschitz, $R(I-hf(t, ·, v))=X$ for $h>0$ sufficiently small, and $f(t,u, ·)$ is Lipschitz continuous, we show that the iterative scheme $u_n+1=u_n+hf((n+1)Δ t, u_n+1, u_n)$, $n=0,1,…, N-1$, $Δ t=T/N$, is stable and consistent, and hence convergent. Applications to systems of evolutionary PDEs are presented and the computational advantages of the semi-implicit method are pointed out.

ISO 690:

Spigler, R., Vianello, M. 1994. Semi-implicit discretization of abstract evolution equations. In Tatra Mountains Mathematical Publications, vol. 4, no.1, pp. 207-212. 1210-3195.

APA:

Spigler, R., Vianello, M. (1994). Semi-implicit discretization of abstract evolution equations. Tatra Mountains Mathematical Publications, 4(1), 207-212. 1210-3195.