Convergence rate estimates for iterative solutions of the biharmonic equation

Decay estimates of solutions to the IBq equation

‎In this paper we focus on the Cauchy problem for the generalized‎ ‎IBq equation with damped term in $n$-dimensional space‎. ‎We establish the global existence and decay estimates of solution with $L^q(1leq qleq 2)$ initial value‎, ‎provided that the initial value is suitably small‎. ‎Moreover‎, ‎we also show that the solution is asymptotic to the solution $u_L$ to the corresponding linear equa...

Superlinear Convergence Estimates for a Conjugate Gradient Method for the Biharmonic Equation

The method of Muskhelishvili for solving the biharmonic equation using con-formal mapping is investigated. In CDH] it was shown, using the Hankel structure, that the linear system in Musk] is the discretization of the identity plus a compact operator, and therefore the conjugate gradient method will converge superlinearly. Estimates are given here of the superlinear convergence in the cases whe...

On Univalent Solutions of the Biharmonic Equation

On The Mean Convergence of Biharmonic Functions

Let denote the unit circle in the complex plane. Given a function , one uses t usual (harmonic) Poisson kernel for the unit disk to define the Poisson integral of , namely . Here we consider the biharmonic Poisson kernel for the unit disk to define the notion of -integral of a given function ; this associated biharmonic function will be denoted by . We then consider the dilations ...

Convergence of iterative methods applied to Burgers-Huxley equation