1 edition of Generalized collocations methods found in the catalog.
|The Physical Object|
|Pagination||xvi, 88 p. :|
|Number of Pages||57|
|2||Modeling and simulation in science, engineering and technology|
nodata File Size: 4MB.
Culham and Varga have presented the most convincing evidence in favor of Galerkin methods. The principal argument is that better answers can be obtained for the same computational effort than by finite-difference methods.
Contents Mathematical Models and Problems in Applied Sciences Lagrange and Sinc Collocation Interpolation Methods Nonlinear Initial Value Problems in Unbounded Domains Nonlinear Initial-Boundary Value Problems in One Space Dimension Initial-Boundary Value Problems in Two Space Dimensions Additional Mathematical Tools for Nonlinear Problems Appendix: Scientific Programs Description This book examines various mathematical tools--based on generalized collocation methods--to solve nonlinear problems related to partial differential and integrodifferential equations.
An example of seawater Generalized collocations methods into coastal aquifers is solved to illustrate the applicability of the method.
br000095 Mehdi Dehghan, Abbas Saadatmandi, Chebyshev finite difference method for Fredholm integro-differential equation, Int. Numerous real-world applications, including wave motion models, vehicular traffic flow, and population dynamics This book examines various mathematical tools—based on generalized collocation methods—to solve nonlinear problems related to partial differential and integro-differential equations.
Generalized Collocation Methods is written for an interdisciplinary audience of graduate students, engineers, scientists, and applied mathematicians with an interest in modeling real-world systems by differential or operator equations. We present polynomials based collocation methods for Generalized Abel's integral equations.
Atkinson, The Numerical Solution of Integral equations of Second Kind HandbookCambridge University Press, The Edinburgh Building, Cambridge C132 8RU, UK, 1997. We develop spectral collocation methods for fractional differential equations with variable order with two end-point singularities.
The volume is written for an interdisciplinary audience: graduate students, engineers, scientists, and applied mathematicians interested in modeling real-world systems by differential or operator equations. 1690060303 M3 - Article AN - SCOPUS:84985359611 VL - 6 SP - 215 EP - 230 JO - Numerical Methods for Generalized collocations methods Differential Equations JF - Numerical Methods for Partial Differential Equations Generalized collocations methods - 0749-159X IS - 3 ER. The result is a very efficient solution procedure for parabolic partial differential equations.
Collocation method in sense of Atkinson's approach Atkinson, 2016 is applied to get the approximate solution of Generalized Abel's integral equations. Baharifard, Solving a laminar boundary layer equation with the rational Gegenbauer functions, Appl. Smith-Miles, Solving boundary value problems, integral and integro-differential equations using Gagenbauer integration series, J.
Pipkin, A Course on Integral Equations, Spronger- Verlag, New York, 1991. Potential readers, in particular university students interested in applying mathematics who wish to become acquainted with the enormous power of scientific computing, are advised to read this well-written textbook, certainly if they already possess Mathematica skills.
Covered are specific problems and models related to vehicular traffic flow, population dynamics, wave phenomena, heat convection and diffusion, transport phenomena, and pollution.
Numerical results show that the proposed method works well and achieve good accuracy even for less number of polynomials.
The convergence analysis of the presented method is also established.