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Lyapunov functions are an important tool for the determination of the domain of attraction of an equilibrium point of a given ordinary differential equation. The Radial Basis Functions collocation method is one of the numerical methods to construct Lyapunov functions. This method has been improved by combining it with a refinement algorithm to reduce the number of collocation points required in the construction process, as well as a verification that the constructed function is a Lyapunov function. In this paper, we propose a combination of both methods in one, called the combination method. This method constructs a Lyapunov function with the refinement algorithm and then verifies its properties rigorously. The method is illustrated with examples.

Combination of Refinement and Verification for the Construction of Lyapunov Functions using Radial Basis Functions