Analyses of spline collocation methods for parabolic and hyperbolic problems in two space variables
SIAM Journal on Numerical Analysis
Spectral methods in MatLab
Numerical solution of a Fredholm integro-differential equation modelling neural networks
Applied Numerical Mathematics
Numerical convergence of a one step approximation of an integro-differential equation
Applied Numerical Mathematics
Fast and efficient numerical methods for an extended Black-Scholes model
Computers & Mathematics with Applications
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In this article, we consider a nonlinear integro-differential equation that arises in a @q@?-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.