Rigorous numerics for nonlinear heat equations in the complex plane of time

Abstract In this paper, we introduce a method for computing rigorous local inclusions of solutions Cauchy problems nonlinear heat equations complex time values. The proof is constructive and provides explicit bounds the inclusion solution problem, which rewritten as zero-finding problem on certain Banach space. Using map operator, construct simplified Newton operator show that it has unique fixed point. point together with its problem. technique then applied iteratively to compute over long intervals. This used prove existence branching singularity in equation. Finally, an approach based Lyapunov–Perron calculating part center-stable manifold open set converge zero, hence yielding global plane time.