Numerical approximation of a convolution model of \(\dot{\theta}\)-neuron networks. (English) Zbl 1208.65180

Summary: In this article, we consider a nonlinear integro-differential equation that arises in a \(\dot{\theta}\)-neural networks modeling. We analyze boundedness and invertibility of the model operator, construct approximate solutions using piecewise polynomials in space, and estimate the theoretical convergence rate of such spatial approximations. We present some numerical experimental results to demonstrate the scheme.


65R20 Numerical methods for integral equations
45K05 Integro-partial differential equations
45G10 Other nonlinear integral equations
92B20 Neural networks for/in biological studies, artificial life and related topics


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