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This paper proposes an efficient symbolic-numeric method to compute theintegrals in the successive Galerkin approximation (SGA) of theHamilton-Jacobi-Bellman (HJB) equation. A solution of the HJB equation is firstapproximated with a linear combination of the Hermite polynomials. Thecoefficients of the combination are then computed by iteratively solving alinear equation, which consists of the integrals of the Hermite polynomialsmultiplied by nonlinear functions. The recursive structure of the Hermitepolynomials is inherited by the integrals, and their recurrence relations canbe computed by using the symbolic computation of differential operators. Byusing the recurrence relations, all the integrals can be computed from a partof them that are numerically evaluated. A numerical example is provided to showthe efficiency of the proposed method compared to a standard numericalintegration method.

Symbolic-Numeric Computation of Integrals in Successive Galerkin Approximation of Hamilton-Jacobi-Bellman Equation