3 edition of **Quasilinearization and nonlinear boundary-value problems** found in the catalog.

Quasilinearization and nonlinear boundary-value problems

Richard Ernest Bellman

- 146 Want to read
- 17 Currently reading

Published
**1965**
by Rand Corp. in Santa Monica, Calif
.

Written in English

- Nonlinear boundary value problems -- Numerical solutions,
- Programming (Mathematics)

**Edition Notes**

Statement | [by] Richard E. Bellman and Robert E. Kalaba. |

Series | Modern analytic and computational methods in science and mathematics, [3], Modern analytic and computational methods in science and mathematics ;, v. 3., Rand Corporation research study. |

Contributions | Kalaba, Robert E., joint author. |

Classifications | |
---|---|

LC Classifications | AS36 .R3 R-438 |

The Physical Object | |

Pagination | ix, 206 p. |

Number of Pages | 206 |

ID Numbers | |

Open Library | OL5937733M |

LC Control Number | 65005980 |

The existence, uniqueness and quadratic convergence of the sequence follows from the corresponding convexity of the functions over a sufficiently small interval.. The method of quasi-linearization finds application in the solution of two-point and multi-point boundary value problems for linear and non-linear ordinary differential equations, boundary value problems for elliptic . Bellman RE Kalaba RE () Quasilinearization and Nonlinear Boundary-Value Problems, American Elsevier New York View all references, and .

In earlier papers we have shown that many problems in orbit determination, system identification, vector cardiology, and so on can be considered to be nonlinear multi-point boundary-value prob- lems. Quasilinearization offers an effective computational method of solution. When the number of conditions on the solution exceeds. A numerical method is proposed by wavelet-Galerkin and quasilinearization approach for nonlinear boundary value problems. Quasilinearization technique is applied to linearize the nonlinear differential equation and then wavelet-Galerkin method is implemented to linearized differential equations. In each iteration of quasilinearization technique, solution is updated by .

A MODIFIED QUASILINEARIZATION CONCEPT FOR SOLVING THE NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEM By Jay M. Lewallen Manned Spacecraft Center SUMMARY A new quasilinearization method, referred to as the Modified Quasilinearization Method, is proposed for numerically solving the nonlinear two -point boundary value problem. Quasilinearization technique has been applied to a general nonlinear Lidstone boundary value problem for the construction of a sequence of its approximate solutions {x n (t)}.Sufficient conditions for the linear as well as quadratic convergence of {x n (t)} to the unique solution x ∗ (t) of the boundary value problem have been practice one always .

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Quasilinearization and Nonlinear Boundary-Value Problems. Modern Analytic and Computational Methods in Science and Mathematics. Volume Three (3) [Bellman and Kalaba] on *FREE* shipping on qualifying offers. Quasilinearization and nonlinear boundary-value problems (Modern analytic and computational methods in science and mathematics) First Edition Edition.

by Richard Ernest Bellman (Author) ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of a book Manufacturer: Richard Ernest Bellman.

Quasilinearization and Nonlinear Boundary-Value Problems. Modern Analytic and Computational Methods in Science and Mathematics. Volume Three (3) by Bellman, R.E. and R.E. Kalaba and a great selection of related books, art and collectibles available now at. An introduction to quasilinearization for both those solely interested in the analysis and those primarily concerned with applications.

The Report Quasilinearization and nonlinear boundary-value problems book chapters on: (1) the Riccati Equation; (2) two-point boundary-value problems for second-order differential equations.

Quasilinearization and nonlinear boundary-value problems Bellman R., Kalaba R. Modern electronic computers can provide the numerical solution of systems of one thousand simultaneous nonlinear ordinary differential equations, given a complete.

The Riccati equation --Two-point boundary-value problems for second-order differential equations --Monotone behavior and differential inequalities --systems of differential equations, storage and differential approximation --Partial differential equations --Applications in physics, engineering, and biology --Dynamic programming and quasilinearization --Appendices.

Generalized Quasilinearization for Nonlinear Problems / Edition 1 higher order of convergence, and other contexts. Then moves on to second-order boundary value problems and extensions to a variety of differential equations such as delay, stochastic, integro-differential, differential equations in a Banach space, and dynamic systems on a Price: $ This book emphasizes that the invariant imbedding approach reformulates the original boundary-value problem into an initial value problem by introducing new variables or parameters, while the quasilinearization technique represents an.

TY - BOOK AU - Andrzej Granas AU - Ronald Guenther AU - John Lee TI - Nonlinear boundary value problems for ordinary differential equations PY - CY - Warszawa PB - Instytut Matematyczny Polskiej Akademi Nauk AB - CommentsThis tract is intended to be accessible to a broad spectrum of readers.

Those with out much previous experience with differential. Generalized Quasilinearization Method for Nonlinear Boundary Value Problems with Integral Boundary Conditions ∗ Li Suna, b, Mingru Zhoub, Guangwa Wangb,† aSchool of Mechanics and Civil Engineering, China University of Mining & Technology, XuzhouPR China bSchool of Mathematics, Xuzhou Normal University, XuzhouPR China Abstract.

Multi-point nonlinear boundary value problems, which take into account the boundary data at intermediate points of the interval under consideration, have been receiving considerable attention [20{23].

Eloe and Y. Gao [24] discussed the quasilinearization method for a three-point boundary value problem. Ahmad. Abstract. Among the popular and successful techniques for solving boundary-value problems for nonlinear, ordinary differential equations (ODE) are quasilinearization and the Galerkin procedure.

In this note, it is demonstrated that utilizing the Galerkin criterion followed by the Newton-Raphson scheme results in the same iteration process as. through Quasilinearization. Our main concentration on the following type of nonlinear boundary value problems defined in the interval [a, b].

yt ftyy yn, n 1 (1) subject to boundary conditions 12 1 3 12 1 3,, n n n n. ya y a ya y a yb y b yb y b. Get this from a library. Quasilinearization and nonlinear boundary-value problems.

[Richard Bellman; Robert E Kalaba]. In this chapter quasilinearization is used for system identification (References 1–9) using the measurements to formulate the problem as a multipoint boundary-value problem.

The least-squares criterion is used to estimate the unknown initial conditions and/or unknown parameters. To tackle the nonlinearity, we use the quasilinearization process Bellman RE Kalaba RE () Quasilinearization and Nonlinear Boundary-Value Problems, American Elsevier New York, and to handle the delay term, we use the Taylor series Cunningham WJ () Introduction to Nonlinear Analysis, McGraw-Hill Book Company, Inc New York.

In the limit. A novel computational approach known as pseudospectral quasilinearization (SQLM) is employed to tackle the two-point boundary value problem describing the reactivity behaviour of porous catalyst particles subject to both internal mass concentration gradients and temperature gradients, in endothermic or exothermic catalytic reactions.

A comparison with the numerical. This paper studies the existence and uniqueness of solutions for a nonlocal singular boundary value problem of second-order integro-differential equations in weighted spaces.

The method of quasilinearization is applied to obtain monotone sequences of approximate solutions converging uniformly and quadratically to a unique solution of the problem at hand.

An illustrative. Quasilinearization provides an effective computational tool for the solution of a wide class of nonlinear two-point and multi-point boundary-value problems; e.g., Euler equations, orbit determination, partial differential equations, vectorcardiology and system identification.

If the respective nonlinear equation can be reduced to a quasi-linear one with a non-resonant linear part and both equations are equivalent in some domain, and if solutions of the quasi-linear problem lie in, then the original problem has a solution.

We then say that the original problem allows for quasilinearization. Quasilinearization and Approximate Quasilinearization for Multipoint Boundary Value Problems RAVI P.

AGARWAL Department of Mathematics, National University of Singapore, Kent Ridge, Singapore Submitted by C. L. Dolph 1. INTRODUCTION In this paper, we shall consider the following nth-order ordinary dif.Method of Quasilinearization for Boundary Value Problems for Functional Differential Equations (V Lakshmikantham & N Shahzad) Existence Principles for Nonlinear Operator Equations (D O'Regan) Sturmian Theory and Oscillation of a Third Order Linear Difference Equation (A Peterson) and other papers; Readership: Researchers in applied mathematics.Objective of our paper is to present the Haar wavelet based solutions of boundary value problems by Haar collocation method and utilizing Quasilinearization technique to resolve quadratic nonlinearity in y.

More accurate solutions are obtained by wavelet decomposition in the form of a multiresolution analysis of the function which represents solution of boundary value problems.