6. References

AD19

P. Assari and M. Dehghan. A meshless local discrete Galerkin (MLDG) scheme for numerically solving two-dimensional nonlinear Volterra integral equations. Appl Math Comput., 350:249–265, 2019.

BMCK10

V. Bayona, M. Moscoso, M. Carretero, and M. Kindelan. Rbf-fd formulas and convergence properties. J Comput Phys., 229(22):8281–8295, 2010.

BMK12

V. Bayona, M. Moscoso, and M. Kindelan. Gaussian RBF-FD weights and its corresponding local truncation errors. Eng Anal Bound Elem., 36(9):1361–1369, 2012.

BF79

D. Best and N. Fisher. Efficient simulation of the von Mises distribution. J R Stat Soc Ser C Appl Stat., 28(2):152–157, 1979.

BMH04

E. Brown, J. Mohelis, and P. Holmes. On the phase reduction and response dynamics of neural oscillator populations. Neural Comput., 16(4):673–715, 2004.

DA19

M. Dehghan and M. Abbaszadeh. Error analysis and numerical simulation of magnetohydrodynamics (MHD) equation based on the interpolating element free Galerkin (IEFG) method. Appl Numer Math., 137:252–273, 2019.

DP19

M. Delkhosh and K. Parand. Generalized pseudospectral method: Theory and applications. J Comput Sci., 34:11–32, 2019.

Fas07

G. E. Fasshauer. Meshfree approximation methods with MATLAB. Volume 6. World Scientific, 2007.

Fas05

GE Fasshauer. Rbf collocation methods as pseudospectral methods. WIT Trans Modelling Simul., 2005.

FFBB16

N. Flyer, B. Fornberg, V. Bayona, and G. A. Barnett. On the role of polynomials in RBF-FD approximations: I. Interpolation and accuracy. J Comput Phys., 321:21–38, 2016.

For88

B. Fornberg. Generation of finite difference formulas on arbitrarily spaced grids. Math. Comput., 51(184):699–706, 1988.

FLP13

B. Fornberg, E. Lehto, and C. Powell. Stable calculation of Gaussian-based RBF-FD stencils. Comput Math Appl., 65(4):627–637, 2013.

GPH+10

D. Grag, M. Patterson, W. W. Hager, A. V. Rao, D. A. Benson, and G. T. Huntington. A unified framework for the numerical solution of optimal control problems using pseudospectral methods. Automatica., 46(11):1843–1851, 2010.

HRBPR19

A. Hadian-Rasanan, N. Bajelan, K. Parand, and J. A. Rad. Simulation of nonlinear fractional dynamics arising in the modeling of cognitive decision making using a new fractional neural network. Math Meth Appl Sci., 43(3):1437–1466, 2019.

HR84

J. Hindmarsh and R. Rose. A model of neuronal bursting using three coupled first order differential equations. Proc R Soc Lond B., 221(1222):87–102, 1984.

HH52

A. L. Hodgkin and A. F. Huxley. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol., 117(4):500–544, 1952.

Izh07

E. M. Izhikevich. Dynamical Systems in Neuroscience. MIT Press, 2007.

IF06

E. M. Izhikevich and R. Fitzhugh. FitzHugh-Nagumo model. Scholarpedia, 1(9):1349, 2006.

JS18

A. Jafarabadi and E. Shivanian. Numerical simulation of nonlinear coupled Burgers’ equation through meshless radial point interpolation method. Eng Anal Bound Elem., 95:187–199, 2018.

KAK+20

S. Kumar, A. Ahmadian, R. Kumar, D. Kumar, J. Singh, D. Baleanu, and M. Salimi. An efcient numerical method for fractional SIR epidemic model of infectious disease by using Bernstein wavelets. Mathematics., 8(4):558, 2020.

LD20

S. Latifi and M. Delkhosh. Generalized Lagrange Jacobi‐Gauss‐Lobatto vs Jacobi‐Gauss‐Lobatto collocation approximations for solving (2 + 1)‐dimensional Sine‐Gordon equations. Math Meth Appl Sci., 43(4):2001–2019, 2020.

MHRL+20

M. M. Moayeri, A. Hadian-Rasanan, S. Latifi, K. Parand, and J. A. Rad. An efficient space-splitting method for simulating brain neurons by neuronal synchronization to control epileptic activity. Eng Comput., 2020. doi:https://doi.org/10.1007/s00366-020-01086-9.

MRP21

M. M. Moayeri, J. A. Rad, and K. Parand. Desynchronization of stochastically synchronized neural populations through phase distribution control: a numerical simulation approach. Nonlinear Dyn., 104:2363–2388, 2021.

MD20

V. Mohammadi and M. Dehghan. Generalized moving least squares approximation for the solution of local and non-local models of cancer cell invasion of tissue under the effect of adhesion in one- and two-dimensional spaces. Comput Biol Med., 2020. doi:https://doi.org/10.1016/j.compbiomed.2020.103803.

MFM18

B. Monga, G. Froyland, and J. Moehlis. Synchronizing and desynchronizing neural populations through phase distribution control. 2018 Annual American Control Conference (ACC), pages 2808–2813, 2018.

MM19a

B. Monga and J. Moehlis. Optimal phase control of biological oscillators using augmented phase reduction. Biol Cybern., 113(1):161–178, 2019.

MM19b

B. Monga and J. Moehlis. Phase distribution control of a population of oscillators. Physica D., 398:115–129, 2019.

MWMM18

B. Monga, D. Wilson, T. Matchen, and J. Moehlis. Phase reduction and phase-based optimal control for biological systems: a tutorial. Biol Cybern., 113:11–46, 2018.

PLDM18

K. Parand, S. Latifi, M. Delkhosh, and M. M. Moayeri. Generalized Lagrangian Jacobi Gauss collocation method for solving unsteady isothermal gas through a micro-nano porous medium. Eur Phys J Plus., 2018.

PLMD18

K. Parand, S. Latifi, M. M. Moayeri, and M. Delkhosh. Generalized Lagrange Jacobi Gauss-Lobatto (GLJGL) collocation method for solving linear and nonlinear Fokker-Planck equations. Commun Theor Phys., 69:519–531, 2018.

PMLR19

K. Parand, M. M. Moayeri, S. Latifi, and J. A. Rad. Numerical study of a multidimensional dynamic quantum model arising in cognitive psychology especially in decision making. Eur Phys J Plus., 2019.

RHookLS18

J. A. Rad, J. Höök, E. Larsson, and L. Von Sydow. Forward deterministic pricing of options using Gaussian radial basis functions. J Comput Sci., 24:209–217, 2018.

RH89

R. Rose and J. Hindmarsh. The assembly of ionic currents in a thalamic neuron I. The three-dimensional model. Proc R Soc Lond B., 237():267–288, 1989.

RT04

J. Rubin and D. Terman. High frequency stimulation of the subthalamic nucleus eliminates pathological thalamic rhythmicity in a computational model. J Comput Neurosci., 16(3):211–235, 2004.

SVHL15

A. Safdari-Vaighani, A. Heryudono, and E. Larsson. A radial basis function partition of unity collocation method for convection–diffusion equations arising in financial applications. J Sci Comput., 64(2):341–367, 2015.

SVLH18

A. Safdari-Vaighani, E. Larsson, and A. Heryudono. Radial basis function methods for the Rosenau equation and other higher order PDEs. J Sci Comput., 75(3):1555–1580, 2018.

SMN+15

B. Sarler, N. Massarotti, P. Nithiarasu, B. Mavrič, and B. Šarler. Local radial basis function collocation method for linear thermoelasticity in two dimensions. Int J Numer Method H., 2015.

Sar05

S. A. Sarra. Adaptive radial basis function methods for time dependent partial differential equations. Appl Numer Math., 54(1):79–94, 2005.

Sau12

T. Sauer. Numerical Analysis. Pearson Education, 2012.

SL16

V. Shcherbakov and E. Larsson. Radial basis function partition of unity methods for pricing vanilla basket options. Comput Math Appl., 71(1):185–200, 2016.

SJ18a

E. Shivanian and A. Jafarabadi. An improved meshless algorithm for a kind of fractional cable problem with error estimate. Chaos Solitons Fractals., 110:138–151, 2018.

SJ18b

E. Shivanian and A. Jafarabadi. The spectral meshless radial point interpolation method for solving an inverse source problem of the time-fractional diffusion equation. Appl Numer Math., 129:1–25, 2018.

Tol00

A. I. Tolstykh. On using rbf-based differencing formulas for unstructured and mixed structured-unstructured grid calculations. In Proceedings of the 16th IMACS world congress, volume 228, 4606–4624. Lausanne, 2000.

Wen95

H. Wendland. Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree. Adv Comput Math., 4(1):389–396, 1995.

WM16

D. Wilson and J. Moehlis. Isostable reduction with applications to time-dependent partial differential equations. Phys Rev E., 94:012211, 2016.

WM14

D. Wlison and J. Moehlis. Optimal chaotic desynchronization for neural populations. SIAM J Appl Dyn Syst., 13(1):276–305, 2014.