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Your search keyword '"Cattani, Carlo"' showing total 9 results
Start Over Author "Cattani, Carlo" Topic haar wavelets
9 results on '"Cattani, Carlo"'

3. Wavelet Analysis of Spike Train in the Fitzhugh Model

Author

Cattani, Carlo, Scalia, Massimo, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Gavrilova, Marina L., editor, and Tan, C. J. Kenneth, editor

Published
2009
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5. Wavelet Analysis of Pulses in the Fitzhugh Model

Author

Cattani, Carlo, Scalia, Massimo, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Gervasi, Osvaldo, editor, Murgante, Beniamino, editor, Laganà, Antonio, editor, Taniar, David, editor, Mun, Youngsong, editor, and Gavrilova, Marina L., editor

Published
2008
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6. On a numerical method based on wavelets for Fredholm‐Hammerstein integral equations of the second kind.

Author

Micula, Sanda and Cattani, Carlo

Subjects
*INTEGRAL equations, *VOLTERRA equations, *WAVELETS (Mathematics), *NONLINEAR analysis, *ERROR analysis in mathematics
Abstract

In this paper, we consider a special kind of nonlinear integral equations, Fredholm‐Hammerstein equations. As done before we use an equivalent reformulation, for which collocation methods are more efficient. For the alternative equation, we use a collocation method based on Haar wavelets to approximate the solution. We discuss the convergence and error analysis of the method, showing that, at the collocation nodes, the order of convergence is higher than expected. The paper concludes with numerical examples, which illustrate the good approximations, conclusions, and ideas for future work in this area. [ABSTRACT FROM AUTHOR]

Published
2018
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7. A numerical scheme for a class of generalized Burgers' equation based on Haar wavelet nonstandard finite difference method.

Author

Verma, Amit Kumar, Rawani, Mukesh Kumar, and Cattani, Carlo

Subjects
*BURGERS' equation, *FINITE difference method, *FINITE differences, *COLLOCATION methods, *ANALYTICAL solutions
Abstract

Solving Burgers' equation always posses challenges for a small value of viscosity. Here we present a numerical method based on the Haar wavelet collocation method coupled with a nonstandard finite difference (NSFD) scheme for a class of generalized Burgers' equation. In the solution process, the time derivative is discretized by the NSFD scheme and the spatial derivatives are approximated by the Haar wavelets series. The nonlinear terms are linearized with the help of the quasilinearisation process. We illustrate the efficiency of the proposed method by solving several test problems and report their L 2 -error and L ∞ -error norms. The derived method is quite easy to implement compared to the other methods. Also, the error analysis of the current method is discussed. It is also observed that for the small number of grid points, the current method produces results that are in great agreement with the analytical solutions. [ABSTRACT FROM AUTHOR]

Published
2021
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8. Haar Wavelet Series Method for Solving Simultaneous Proportional Delay Differential Equations

Author

Hussain, Basharat, Afroz, Afroz, Kacprzyk, Janusz, Series Editor, Gomide, Fernando, Advisory Editor, Kaynak, Okyay, Advisory Editor, Liu, Derong, Advisory Editor, Pedrycz, Witold, Advisory Editor, Polycarpou, Marios M., Advisory Editor, Rudas, Imre J., Advisory Editor, Wang, Jun, Advisory Editor, Singh, Jagdev, editor, Anastassiou, George A., editor, Baleanu, Dumitru, editor, Cattani, Carlo, editor, and Kumar, Devendra, editor

Published
2023
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9. A novel hybrid approach for computing numerical solution of the time-fractional nonlinear one and two-dimensional partial integro-differential equation.

Author

Rawani, Mukesh Kumar, Verma, Amit Kumar, and Cattani, Carlo

Subjects
*INTEGRO-differential equations, *FINITE differences, *COLLOCATION methods, *QUASILINEARIZATION, *COUPLING schemes
Abstract

In this article, we develop a computational technique for solving the nonlinear time-fractional one and two-dimensional partial integro-differential equation with a weakly singular kernel. For the approximation of spatial derivatives, we apply the Haar wavelets collocation method whereas, for the time-fractional derivative, we use the nonstandard finite difference (NSFD) scheme. We implement the quasilinearization technique to deal with the nonlinear term and product trapezoidal rule for the approximation of integral term. To demonstrate the accuracy of the method, we investigate several test problems and report the accuracy of the method. The convergence and stability of the proposed method are also discussed. • The proposed scheme is based on Haar wavelet method coupled with NSFD scheme. • Convergence and stability of the proposed method are discussed. • Presence of denominator function provides flexibility to improve the accuracy further. • To deal with the nonlinear terms, we use quasilinearization technique. [ABSTRACT FROM AUTHOR]

Published
2023
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