منابع مشابه
Value Problems for Ordinary Differential
The parallel solution of Initial Value Problems for Ordinary Diierential Equations has become an active area of research during the past few years. We brieey survey the recent developments in this area, with particular emphasis on traditional forward-step methods that ooer the potential for eeective small-scale parallelism on currently existing machines.
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Consider a second-order linear 2-point boundary value problem (BVP) −z + p(x)z + q(x)z = r(x) (10.1) z(a) = α (10.2) z(b) = β (10.3) where p(x), q(x) and r(x) are given. By defining y(x) := [z(x), z (x)] T , the problem can be changed into a first-order differential system y = 0 1 q(x) p(x) y + 0 −r(x) (10.4) y 1 (a) − α = 0 (10.5) y 2 (b) − β = 0. (10.6) Remark. In general, a linear 2-point BV...
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The goal of this book is to expose the reader to modern computational tools for solving differential equation models that arise in chemical engineering, e.g., diffusion-reaction, mass-heat transfer, and fluid flow. The emphasis is placed on the understanding and proper use of software packages. In each chapter we outline numerical techniques that either illustrate a computational property of in...
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Compared to standard numerical methods for initial value problems (IVPs) for ordinary diierential equations (ODEs), validated methods for IVPs for ODEs have two important advantages: if they return a solution to a problem, then (1) the problem is guaranteed to have a unique solution, and (2) an enclosure of the true solution is produced. The authors survey Taylor series methods for validated so...
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We may be interested in the solution u(t) in a finite interval [t0, T ] or in the semi-infinite interval t ≥ t0. In most of this lecture f and u are real-valued functions. A generalization to vector-valued functions is important in applications and will be discussed at the end of the lecture. Numerical methods for the solution of the initial value problem (1)-(2) generate a sequence of values o...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1983
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700026149