Generalized Collocation Methods Solutions to Nonlinear Problems (Modeling and Simulation in Science, Engineering and Technology) by Nicola Bellomo

Cover of: Generalized Collocation Methods | Nicola Bellomo

Published by Birkhäuser Boston .

Written in English

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Subjects:

  • Calculus & mathematical analysis,
  • Mathematics for scientists & engineers,
  • Mathematics,
  • Applied,
  • Science/Mathematics,
  • Differential Equations,
  • Mathematical Physics,
  • Mathematica,
  • Mathematics / Applied,
  • collocation methods,
  • convection-diffusion models,
  • differential quadrature method,
  • hydrodynamic models,
  • initial-boundary value problems,
  • nonlinear evolution equations,
  • pollution,
  • population dynamics,
  • reaction-diffusion models,
  • transport phenomena,
  • wave phenomena models

Book details

The Physical Object
FormatHardcover
Number of Pages196
ID Numbers
Open LibraryOL8074885M
ISBN 10081764525X
ISBN 109780817645250

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This book examines various mathematical tools—based on generalized collocation methods—to solve nonlinear problems related to partial differential and integro-differential equations. Covered are specific problems and models related to vehicular traffic flow, Brand: Birkhäuser Basel.

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. The work may be used as a supplementary textbook in graduate courses on modeling and nonlinear differential.

Generalized Collocation Methods: Solutions to Nonlinear Problems (Modeling and Simulation in Science, Engineering and Technology) - Kindle edition by Bellomo, Nicola, Lods, Bertrand, Revelli, Roberto, Ridolfi, Luca.

Download it once and read it on your Kindle device, PC, phones Generalized Collocation Methods book tablets. Use features like bookmarks, note taking and highlighting while reading Generalized 3/5(1).

Buy Generalized Collocation Methods: Solutions to Nonlinear Problems (Modeling and Simulation in Science, Engineering and Technology) on Cited by: Get this from a library. Generalized collocation methods: solutions to nonlinear problems.

[N Bellomo;] -- "This book examines various mathematical tools - based on generalized collocation methods - to solve nonlinear problems related to partial differential and integrodifferential equations. Covered are. We first study the existence, uniqueness, and regularity properties of solutions to a generalized version of the auto-convolution Volterra integral equation of the second kind.

These results are then used to establish the optimal global and local (super) convergence properties of piecewise polynomial collocation solutions for such integral Cited by: 6. This book examines various mathematical tools--based on generalized collocation methods--to solve nonlinear problems related to partial differential and integrodifferential equations.

Covered are specific problems and models related to vehicular traffic flow, population dynamics, wave phenomena, heat convention and diffusion, transport phenomena, and pollution.

A Collocation Method for Numerical Solution of the Generalized Burgers-Huxley Equation Article (PDF Available) August with Reads How we measure 'reads'.

This book examines various mathematical tools--based on generalized collocation methods--to solve nonlinear problems related to partial differential and integrodifferential equations.

Covered are specific problems and models related to vehicular traffic flow, population dynamics, wave phenomena, heat convention and diffusion, transport. 4 1 The collocation method for ODEs: an Generalized Collocation Methods book We see that the equations () and () define, as asserted above, a continuous implicit Runge–Kutta (CIRK) method for the initial-value prob- lem (): its m stage values Y n,i are given by the solution of the nonlinear algebraic systems (), and () defines the approximation u h for eachFile Size: KB.

A Chebyshev collocation method for the wave equation in generalized coordinates For the fundamentals of pseudospectral methods the reader is referred to the excellent book. In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral idea is to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree) and a number of points in the domain (called collocation points), and to select that solution which.

Generalized fractional operators are generalization of the Riemann-Liouville and Caputo fractional derivatives, which include Erdélyi-Kober and Hadamard operators as their special cases.

Due to the complicated form of the kernel and weight function in the convolution, it is even harder to design high order numerical methods for differential equations with generalized fractional Author: Qinwu Xu, Zhoushun Zheng.

We develop spectral collocation methods for fractional differential equations with variable order with two end-point singularities. Specifically, we derive three-term recurrence relations for both integrals and derivatives of the weighted Jacobi polynomials of the form $(1+x)^{\mu_1}(1-x)^{\mu_2}P_{j}^{a,b}(x) \,({a,b,\mu_1,\mu_2>-1})$, which leads to the desired differentiation Cited by: The application of generalized collocation methods need to go through the proper analysis of the following, among several ones, items: selection of the type of collocation and of the interpolants; selection of the number n of collocation points; selection of the time step h Cited by: Lagrange and Sinc Collocation Interpolation Methods.

Authors; Authors and affiliations; Nicola Bellomo Ridolfi L. () Lagrange and Sinc Collocation Interpolation Methods. In: Bellomo N., Lods B., Revelli R., Ridolfi L. (eds) Generalized Collocation Methods. Modeling and Simulation in Science, Engineering and Technology.

Birkhäuser Cited by: 1. General linear methods (GLMs) are a large class of numerical methods used to obtain numerical solutions to differential large class of methods in numerical analysis encompass multistage Runge–Kutta methods that use intermediate collocation points, as well as linear multistep methods that save a finite time history of the solution.

John C. Butcher originally. Kadner, "Numerical treatment of integral equations by collocation methods" Num. Math., 10 () pp. – [a10] G. Keller, "Numerical solution of initial-value problems by collocation methods using generalized piecewise functions" Computing, 28 () pp.

– [a11]. This book examines various mathematical toolsbased on generalized collocation methodsto solve nonlinear problems related to partial differential and integro-differential equations.

Covered are specific problems and models related to vehicular traffic flow, population dynamics, wave phenomena, heat convection and diffusion, transport phenomena. A collocation method based on extended cubic B-splines for numerical solutions of the Klein-Gordon equation Alper Korkmaza;, Ozlem Ersoyb, Idiris Dagc a Department of Mathematics, C˘ank r Karatekin University,C˘ank r, Turkey.

The application of generalized collocation methods need to go through the proper analysis of the following, among several ones, items: 30 N. BELLOMO selection of the type of collocation and of the interpolants; selection of the number n of collocation points; selection of the time step h of the integration in by: Numerical methods vary in their behavior, and the many different types of differ-ential equation problems affect the performanceof numerical methods in a variety of ways.

An excellent book for “real world” examples of solving differential equations is that of Shampine, Gladwell, and Thompson [74].File Size: 1MB.

() Jacobi Collocation Methods for Solving Generalized Space-Fractional Burgers’ Equations. Communications on Applied Mathematics and Computation() Legendre–Galerkin Methods for Third Kind VIEs and by: Generalized Collocation Methods Similarly, the choice of the software Mathematica is also related to the personal experience of the authors [24].

Alternative softwares can be used by the reader according to one's own. Collocation Methods Main concepts: Polynomial interpolation, quadrature, collocation methods Construction of one-step methods One-step methods for () can be constructed in a variety of ways.

A natural approach is to integrate both sides of the differential equation over one timestep, y(t+h)−y(t) = Z t+h t f(y(τ))dτ,File Size: KB.

[email protected] first graduate-level textbook to focus on fundamental aspects of numerical methods for stochastic computations, this book describes the class of numerical methods based on generalized polynomial chaos (gPC). These fast, efficient, and accurate methods are an extension of the classical spectral methods of high-dimensional random spaces.

In this paper, Generalized Burgers-Fisher Equation(GBFE) is fully-integrated by using exponential cubic B-Spline collocation method in space and Crank Nicolson method in time. The numerical results are given to illustrate the efficiency of the proposed method and compared with both the exact solutions and some earlier is shown that accuracy is increased with an Cited by: 9.

of boundary methods in the appendix. This book is an extension of the leading author’s earlier books on combined methods based on the theoretical analysis of finite element method (FEM).

However, this book has several distinct features, which are addressed as follows: 1. In this book, the boundary collocation method, which is a form of Trefftz. Many researchers have investigated the analytical and numerical solutions of the generalized Burgers′-Fisher Equation (1) by using several different methods [8–17].For example, Ismail et al.

[] used adomian decomposition method (ADM), Rashidi et al. [] employed homotopy perturbation method (HPM), Nawaz et al. []applied optimal homotopy asymptotic method (OHAM),for Cited by: 8. Nicola Bellomo Professor of Mathematical Physics and Applied Mathematics Generalized collocation methods - Solution to nonlinear problems.

Birkhauser(with B. Lods, R. Revelli, L. Ridolfi.) Generalized Kinetic Models in Applied Sciences, World Scientific(with L. MATLAB code for applying spectral methods to various types of problems is available online. This excellent and very well-written book could be used as a graduate textbook in mathematics and other engineering disciplines.

It would also be a good reference book for active practitioners and researchers of spectral methods. Generalized Runge-Kutta methods specifically devised for the numerical solution of stiff systems of ordinary differential equations are described.

An A-stable method is employed to solve several sample point reactor kinetics problems, explicitly showing. In corpus linguistics, a collocation is a series of words or terms that co-occur more often than would be expected by chance.

In phraseology, collocation is a sub-type of example of a phraseological collocation, as propounded by Michael Halliday, is the expression strong the same meaning could be conveyed by the roughly equivalent powerful tea, this.

Generalized collocation methods: solutions to nonlinear problems [book () Pagina-navigatie: Main; Save publication.

Save as MODS; Export to Mendeley; Save as EndNote; Export to RefWorks; Title: Generalized collocation methods: solutions to nonlinear problems [book review of MR].

Published in: SIAM Review, 52(1), - ISSN Author: J.G. Verwer. a = x x x 0 1 i-1 N x = b 1 φ φ i i-1 ω i-1 ω i x i 3 3 3 3 Figure Geometry for the collo cation solution of sho wing restriction the cubic Hermite p olynomial basis to the subinFile Size: KB.

understanding noun. 1 knowledge of a subject, of how sth works, etc. ADJ. complete, full He showed a full understanding of the sequence of events.| growing | clear, deep, good, profound, proper, sophisticated, thorough, true You need to read more widely to gain a proper understanding of the issue.| adequate, basic, broad, general, sufficient | limited She has only a.

Book. Xiu, Numerical Methods for Stochastic Computations: A Spectral Method Approach, Princeton University Press, ISBNISBN 15 Collocation Methods for Volterra Integral and Related Functional Equations Collocation methods for DDEs: a brief review The book can be divided in a natural way into four parts: In Part I we focus on collocation methods, mostly in piecewise polyno-File Size: KB.

Teaching Collocation book. Read 4 reviews from the world's largest community for readers. This volume contains papers by a number of teachers and theoret /5. This paper is concerned with introducing two wavelets collocation algorithms for solving linear and nonlinear multipoint boundary value problems.

The principal idea for obtaining spectral numerical solutions for such equations is employing third- and fourth-kind Chebyshev wavelets along with the spectral collocation method to transform the differential equation with its boundary Cited by:.

9 Boundary Value Problems: Collocation We now present a different type of numerical method that will yield the approximate solution of a boundary value problem in the form of a function, as opposed to the set of discrete points resulting from the File Size: KB.We initiate the study of collocation methods for NURBS-based isogeometric analysis.

The idea is to connect the superior accuracy and smoothness of NURBS basis functions with the low computational cost of collocation. We develop a one-dimensional theoretical analysis, and perform numerical tests in one, two and three by: methods based on the theoretical analysis of finite element method (FEM).

However, this book has several distinct features, which are addressed as follows: 1. In this book, the boundary collocation method, which is a form of Trefftz method (TM) [], is presented, and referred to as the collocation Trefftz method (CTM).

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