2026 Volume 18 Pages 45-48
For dissipative partial differential equations, convex splitting is a popular method to construct numerical integrators inheriting the dissipation laws. Although the dissipation holds unconditionally, there is also a drawback that the resulting schemes are generally fully implicit and computationally expensive. In this letter, we propose a new method for designing linearly-implicit dissipative integrators, which is inspired by the proximal DC algorithm for composite optimization problems. We then demonstrate the method in the Swift–Hohenberg equation, and provide the numerical evidence that supports the theory.
