An effect iteration algorithm for numerical solution of discrete Hamilton-Jacobi-Bellman equations (Q2574428)

The authors consider the Hamilton-Jacobi-Bellman equation \[ \max_{1\leq\nu\leq m} [A^{(\nu)}u(x)- f^{(\nu)}(x)]= 0,\qquad x\in\Omega \] with the boundary condition \(u(x)= 0\), \(x\in\delta\Omega\), where \(\Omega\) is bounded and smooth, \(f^{(\nu)}(x)\) are functions from \(C^2(\Omega)\) and \(A^{(\nu)}\) are second-order uniformly elliptic operators. Applying finite difference or finite element methods, the authors obtain a discrete Hamilton-Jacobi-Bellman equation. For this discrete equation an algorithm for the numerical solution is proposed and some numerical examples are presented.