# Download Construction of Integration Formulas for Initial Value by P.J.Van Der Houwen PDF

By P.J.Van Der Houwen

ISBN-10: 0720423503

ISBN-13: 9780720423501

ISBN-10: 0720423724

ISBN-13: 9780720423723

Similar mathematics_1 books

Mathematik / Albert Fetzer. 1

Dieses erfolgreiche einf? hrende Lehrbuch liegt nun in der 10. Auflage vor. Es zeichnet sich durch eine exakte und anschauliche Darstellung aus. Der Lehrstoff ist klar gegliedert und intestine strukturiert. Er wird durch eine F? lle von Beispielen und Abbildungen veranschaulicht und vertieft. Zahlreiche Aufgaben mit L?

Probabilistic Expert Systems (CBMS-NSF Regional Conference Series in Applied Mathematics)

Probabilistic specialist platforms emphasizes the fundamental computational rules that make probabilistic reasoning possible in professional platforms. the foremost to computation in those platforms is the modularity of the probabilistic version. Shafer describes and compares the critical architectures for exploiting this modularity within the computation of previous and posterior possibilities.

Surveys in Differential-Algebraic Equations III

The current quantity includes survey articles on a variety of fields of Differential-Algebraic Equations (DAEs), that have common purposes in managed dynamical platforms, specifically in mechanical and electric engineering and a powerful relation to (ordinary) differential equations. the person chapters supply studies, displays of the present nation of study and new thoughts in - Flexibility of DAE formulations - Reachability research and deterministic worldwide optimization - Numerical linear algebra tools - Boundary worth difficulties the consequences are awarded in an obtainable sort, making this ebook appropriate not just for lively researchers but in addition for graduate scholars (with a great wisdom of the elemental ideas of DAEs) for self-study.

Extra info for Construction of Integration Formulas for Initial Value Problems

Example text

In a Taylor series about x = xn. 1. 2) Λχη + h») - h(y(Xn + hn), J>(*»)) J \ ' \x=xn + hn J υ \ / \x=xn = ( l - ^ o ) X ^ ) + (l+ai-/5i)/z„/(xw)+^(l+2ai + 2a2-2^2)^/Xxw) + 1(1+3αι + 6α2 + 6α 3 -6β 3 ) *«/"(*,,) + 2 ί(ΐ4-4αι+12α 2 + 24α3 + 2 4 α 4 - 2 4 ^ 4 ) ^ / ' , , ( ^ ) + 0 ( ^ ) . 1 is easily derived. This table should be interpreted such, that the conditions on ß09 ßl9 . . , βρ together, guarantee consistency of order p. The derivation of the conditions for fifth or higher order consistency are left to the reader.

1. 2, in connection with the application of Newton-Raphson iteration to the trapezoidal rule. 12"). 2) *"y> = h Θ■- A KJ J — χιιη, J ^ ^ j = 0, 1 , . . , m- 3, j? 3) 0j = 9j(h„J(y„)), AJt, = AJt i(h„J(y„)). Note that each integration step requires one evaluation of the Jacobian matrix 7. In particular, when the, coefficient functions A} t and Θ} are polynomials, then the method is said to be explicit; if at least one of these functions is not a polynomial the method is said to be semi-implicit.

10') in a different form. I, and observe that yn+1 is a linear combination of yn and j = 0, 1, . . , m— 1. , are functions of the relaxation parameters ω ; . ,. 10'); hence, consistency and stability conditions are easier satisfied. 10"); these formulas are explicit and require evaluation of the function / a t m points. Such formulas are, in fact, m-point Runge-Kutta formulas. 1). 2, § 1 SINGLE-STEP METHODS Next, we consider the formulas which arise when Newton-Raphson iteration is applied to the trapezoidal rule.