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We establish a novel convergent iteration framework for a weak approximationof general switching diffusion. The key theoretical basis of the proposedapproach is a restriction of the maximum number of switching so as to untangleand compensate a challenging system of weakly coupled partial differentialequations to a collection of independent partial differential equations, forwhich a variety of accurate and efficient numerical methods are available.Upper and lower bounding functions for the solutions are constructed using theiterative approximate solutions. We provide a rigorous convergence analysis forthe iterative approximate solutions, as well as for the upper and lowerbounding functions. Numerical results are provided to examine our theoreticalfindings and the effectiveness of the proposed framework.

Iterative weak approximation and hard bounds for switching diffusion