Implementing an ODE code on distributed memory computers (Q1339300)

The Cauchy problem for a system of differential equations \(y'(t) = f(t, y(t))\), \(y(t_ 0) = y_ 0\) with \(f : [t_ 0, T] \times \mathbb{R}^ m \to \mathbb{R}^ m\) is studied. A continuous-time waveform relaxation method \[ z'{}^{(k + 1)} (t) = G(t, z^{(k + 1)} (t), y^{(n + 1)} (t), y^{(k+1)} (t), y^{(k)}(t)), \] \(z^{(k+1)} (t_ 0) = y_ 0\), \(y^{(0)} (t_ 0) = y_ 0\), \(y^{(k + 1)} (t) = g(t, z^{(k+1)} (t), y^{(t)} (t))\) is adapted for distributed memory parallel computers where \(G : [t_ 0, T] \times \mathbb{R}^{3m} \to \mathbb{R}^ m\), \(g: [t_ 0, T] \times \mathbb{R}^{2m} \to \mathbb{R}^ m\) satisfy \(G(t, y, y, y) = f(t, y)\), \(g(t, y, y) = f(t, y)\). An application to the diffusion Brusselator equation is given.