3 edition of computational complexity of differential and integral equations found in the catalog.
computational complexity of differential and integral equations
Arthur G. Werschulz
Includes bibliographical references (p. -322) and indexes.
|Statement||Arthur G. Werschulz.|
|Series||Oxford mathematical monographs, Oxford science publications|
|LC Classifications||QA372 .W47 1991|
|The Physical Object|
|Pagination||ix, 331 p. ;|
|Number of Pages||331|
|LC Control Number||91017226|
Numerical & Computational Mathematics on the Academic Oxford University Press website Add Algebraic and Differential Topology of Robust Stability to Cart. Edmond A. Jonckheere. Hardcover Arithmetic, Proof Theory, and Computational Complexity $ Add Arithmetic, Proof Theory, and Computational Complexity to Cart. Integral equations form an important class of problems, arising frequently in engineering, and in mathematical and scientific analysis. This textbook provides a readable account of techniques for their numerical solution. The authors devote their attention primarily to efficient techniques using high order approximations, taking particular account of situations where singularities are present.
answer to Ko’s question raised in , we show that an initial value problem given by a polynomial-time computable, Lipschitz continuous function can have a polynomial-space complete solution. The key insight is simple: the Lipschitz condition means that the feedback in the differential equation is weak. We define a class of polynomial-space computation . Introduction. Fast algorithms for solving differential and integral equations are important for large-scale scientific computing. It usually brings down computational complexity for several orders of magnitude. This ability makes many difficult scientific and engineering problems become analyzable through computational methods.
The solution of the nonhomogeneous partial differential equation is therefore approximated by the discretization of the governing equation using the radial polynomial basis function. To avoid the singularity, the minimum order of the radial polynomial basis function must be greater than two for the second order partial differential equations. Information-based complexity studies optimal algorithms and computational complexity for the continuous problems which arise in physical science, economics, engineering, and mathematical finance. IBC has studied such continuous problems as path integration, partial differential equations, systems of ordinary differential equations, nonlinear equations, integral equations, .
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In this book, the theory of the complexity of the solution to differential and integral equations is developed.
The relationship between the worst case setting and other (sometimes more tractable) related settings, such as the average case, probabilistic, asymptotic, and randomized settings, is also by: The computational complexity of differential and integral equations: an information-based approach.
Book Description. This two volume introduction to the computational solution of differential equations uses a unified approach organized around the adaptive finite element method.
It presents a synthesis of mathematical modeling, analysis, and by: Integral equations form an important class of problems, arising frequently in engineering, and in mathematical and scientific analysis. This textbook provides a readable account of techniques for their numerical : L.
Delves, J. Mohamed. The Computational Complexity of Differential and Integral Equations: An Information-Based Approach (Arthur G. Werschulz)Cited by: 1. On the Computational Complexity of Ordinary Differential Equations* KER-I Ko Department of Computer Science, University of Houston, Houston, Texas The computational complexity of the solution y of the differential equation y'(x)=f(x, y(x)), with the initial value y(0)=0, relative to the computational complexity of the function f is.
Computational Complexity of Ordinary Differential Equations Akitoshi KAWAMURA University of Tokyo Ninth International Conference on Computability and Complexity in Analysis Cambridge, UK J 1 / Computational Differential Equation. A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text.
This book covers the following topics in applied mathematics: Linear Algebraic Systems, Vector Spaces and Bases, Inner Products and Norms, Minimization and Least Squares Approximation, Orthogonality, Equilibrium, Linearity, Eigenvalues, Linear Dynamical Systems, Iteration of Linear Systems, Boundary Value Problems in One Dimension, Fourier Series, Fourier Analysis, Vibration and Diffusion in One-Dimensional Media, The Laplace Equation, Complex Analysis.
A problem will be said to have polynomial complexity if it requires less than CNd steps (or units of time) to be solved, where C and d are constants (d is the degree). • Especially, it is said to have – linear complexity when #steps ≤ CN – quadratic complexity when #steps ≤ CN2 – quasi-linear complexity when #steps ≤ Cε N1+ε.
Constructive and Computational Methods for Differential and Integral Equations Symposium, Indiana University February 17–20, Search within book. Front Matter. An integral equation method for generalized analytic functions.
Wolfgang L. Wendland. Under the direction of the Institute for Informatics and Telematics in Pisa, Calcolo publishes original contributions on numerical analysis and its applications, and on the theory of computation. The main focus of the journal is on numerical linear algebra, approximation theory and its applications, numerical solutions of differential and integral equations, computational complexity.
A recent result showed that the cost of solving initial value problems (IVP) for ordinary differential equations (ODE) is polynomial in the number of digits of accuracy. This improves on the classical result of information-based complexity, which predicts exponential cost.
The computational complexity of Volterra integral equations of the second kind and of the first kind is investigated. It is proved that if the kernel functions satisfy the Lipschitz condition, then the solutions of Volterra equations of the second kind are polynomial-space by: computational complexity of IVP for ODE Solving Ordinary Differential Equations I, Computational Mathematics, Vol.
8 (Springer, Berlin, ). A.G. Werschulz, The Computational Complexity of Differential and Integral Equations (Oxford Science, Oxford, ). Google by: Lecture Notes on Numerical Analysis of Nonlinear Equations.
This book covers the following topics: The Implicit Function Theorem, A Predator-Prey Model, The Gelfand-Bratu Problem, Numerical Continuation, Following Folds, Numerical Treatment of Bifurcations, Examples of Bifurcations, Boundary Value Problems, Orthogonal Collocation, Hopf Bifurcation and.
These operators are computed on the subintervals, respectively, and these computations decrease the storage and computational complexity. Using this technique, the integral and differential equations are converted into the solution of system algebraic equations.
Numerical experiments demonstrate the validity and applicability of this by: equations is a common link between all these recent approaches. Advantages of Discrete Differential Modeling The reader will have most probably understood our bias by now: we believe that the systematic construction, inspired by Exterior Calculus, of differential, yet readily discretizable computational.
Computational Mathematics for Differential Equations by N. Kopchenova, I. Maron. Description: This is a manual on solving problems in computational mathematics. The book is intended primarily for engineering students, but may also prove useful for economics students, for graduate engineers, and for postgraduate students and scientific workers in the applied sciences.
CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We investigate the cost of solving initial value problems for differential algebraic equations depending on the number of digits of accuracy requested. A recent result showed that the cost of solving initial value problems (IVP) for ordinary differential equations (ODE) is polynomial in the number of digits.
X.-J. Yang, Local fractional partial differential equations with fractal boundary problems，Advances in Computational Mathematics and its Applications,1 () X.-J. Yang, Expression of generalized Newton iteration method via generalized local fractional Taylor series, Advances in Computer Science and its Applications, 1 () Lucid, self-contained exposition of the theory of ordinary differential equations and integral equations.
Especially detailed treatment of the boundary value problem of second order linear ordinary differential equations. Other topics include Fredholm integral equations, Volterra integral equations, much more. Bibliography.Information-based complexity is a branch of computational complexity and is formulated as an abstract theory with applications in many areas.
Since continuous computational problems are of interest in many fields, information-based complexity has common interests and has greatly benefited from these fields.