Zobrazeno 1 - 10
of 58
pro vyhledávání: '"Lima, Pedro M."'
Publikováno v:
J Nonlinear Sci 34, 74 (2024)
We study solutions to a recently proposed neural field model in which dendrites are modelled as a continuum of vertical fibres stemming from a somatic layer. Since voltage propagates along the dendritic direction via a cable equation with nonlocal so
Externí odkaz:
http://arxiv.org/abs/2406.09222
Autor:
Talaei, Younes, Lima, Pedro M
This paper is concerned with the numerical solution of the third kind Volterra integral equations with non-smooth solutions based on the recursive approach of the spectral Tau method. To this end, a new set of the fractional version of canonical basi
Externí odkaz:
http://arxiv.org/abs/2207.07405
Publikováno v:
Fractal Fract. 5 (2021), no. 4, Art. 219, 15 pp
We introduce a new numerical method, based on Bernoulli polynomials, for solving multiterm variable-order fractional differential equations. The variable-order fractional derivative was considered in the Caputo sense, while the Riemann--Liouville int
Externí odkaz:
http://arxiv.org/abs/2111.07413
We consider a simple neural field model in which the state variable is dendritic voltage, and in which somas form a continuous one-dimensional layer. This neural field model with dendritic processing is formulated as an integro-differential equation.
Externí odkaz:
http://arxiv.org/abs/2003.12761
Publikováno v:
Numer. Algorithms 86 (2021), no. 2, 675--691
We propose a spectral collocation method, based on the generalized Jacobi wavelets along with the Gauss-Jacobi quadrature formula, for solving a class of third-kind Volterra integral equations. To do this, the interval of integration is first transfo
Externí odkaz:
http://arxiv.org/abs/2002.04736
Publikováno v:
Commun. Nonlinear Sci. Numer. Simul. 78 (2019), Art. 104849, 14 pp
We introduce a numerical method, based on modified hat functions, for solving a class of fractional optimal control problems. In our scheme, the control and the fractional derivative of the state function are considered as linear combinations of the
Externí odkaz:
http://arxiv.org/abs/1905.06839
Autor:
Lima, Pedro M., Buckwar, Evelyn
We introduce a new numerical algorithm for solving the stochastic neural field equation (NFE) with delays. Using this algorithm we have obtained some numerical results which illustrate the effect of noise in the dynamical behaviour of stationary solu
Externí odkaz:
http://arxiv.org/abs/1701.03917
Autor:
Lima, Pedro M., Buckwar, Evelyn
In the present paper we are concerned with a numerical algorithm for the approximation of the two-dimensional neural field equation with delay. We consider three numerical examples that have been analysed before by other authors and are directly conn
Externí odkaz:
http://arxiv.org/abs/1511.00717
Autor:
Lima, Pedro M., Buckwar, Evelyn
We are concerned with the numerical solution of a class integro-differential equations, known as Neural Field Equations, which describe the large-scale dynamics of spatially structured networks of neurons. These equations have many applications in Ne
Externí odkaz:
http://arxiv.org/abs/1508.07484
Autor:
Graça, Mario M., Lima, Pedro M.
We discuss a recursive family of iterative methods for the numerical approximation of roots of nonlinear functions in one variable. These methods are based on Newton-Cotes closed quadrature rules. We prove that when a quadrature rule with $n+1$ nodes
Externí odkaz:
http://arxiv.org/abs/1409.2526