A Hybrid Algorithm Based on Optimal Quadratic Spline Collocation and Parareal Deferred Correction for Parabolic PDEs

Figure 3

Stability region (doted area) using implicit Euler integrators for the coarse propagators and explicit Euler integrators for the fine propagators after 2 iterations (a), 3 iterations (b), 4 iterations (c), and 6 iterations (d). In fact, there exists a relatively very small unstable area around the point in (a). The -axis is and the -axis is , where and .

(a)

(b)

(c)

(d)