scholarly journals Modification of Levenberg-Marquardt Algorithm for Solve Two Dimension Partial Differential Equation

2018 ◽  
Vol 26 (7) ◽  
pp. 107-117
Author(s):  
Khalid Mindeel M. Al-Abrahemee ◽  
Rana T. Shwayaa
Keyword(s):  
Neural Network ◽  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Partial Differential ◽  
Two Dimension ◽  
Marquardt Algorithm ◽  
Levenberg Marquardt ◽  
In The Beginning ◽  
Lm Algorithm

In this paper we presented a new way based on neural network has been developed for solutione of two dimension  partial differential equations . A modified neural network use to over passing the Disadvantages of LM algorithm, in the beginning we suggest signaler value decompositions of Jacobin matrix (J) and inverse of Jacobin matrix( J-1), if a matrix rectangular or singular  Secondly, we suggest new calculation of μk , that ismk=|| E (w)||2    look the nonlinear execution equations E(w) = 0 has not empty solution W* and we refer   to the second norm in all cases ,whereE(w):  is continuously differentiable and E(x) is Lipeschitz  continuous, that is=|| E(w 2)- E(w 1)||£ L|| w  2- w  1|| ,where L  is Lipeschitz  constant.

The Comparison of Parameter Identification Methods for Fractional, Partial Differential Equation

2013 ◽  
Vol 210 ◽  
pp. 265-270 ◽  
Author(s):  
Anna Obrączka ◽  
Wojciech Mitkowski
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Parameter Identification ◽  
Numerical Experiments ◽  
Nonlinear Models ◽  
Fractional Partial Differential Equation ◽  
Partial Differential ◽  
Identification Methods ◽  
Marquardt Algorithm ◽  
Levenberg Marquardt

In this paper the parameter identification methods for nonlinear models were compared for fractional, partial differential equation. The compared three methods are: the Levenberg-Marquardt algorithm, the Gauss-Newton algorithm and Nelder-Mead Simplex method. The series of numerical experiments were performed to test their robustness and calculation speed. The result of this tests were presented and described.

Adaptive Diversification and Speciation as Pattern Formation in Partial Differential Equation Models

2011 ◽  
Author(s):  
Michael Doebeli
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Pattern Formation ◽  
Differential Equations ◽  
Adaptive Dynamics ◽  
Partial Differential ◽  
Adaptive Diversification ◽  
Differential Equation Models ◽  
Phenotype Distribution

This chapter discusses partial differential equation models. Partial differential equations can describe the dynamics of phenotype distributions of polymorphic populations, and they allow for a mathematically concise formulation from which some analytical insights can be obtained. It has been argued that because partial differential equations can describe polymorphic populations, results from such models are fundamentally different from those obtained using adaptive dynamics. In partial differential equation models, diversification manifests itself as pattern formation in phenotype distribution. More precisely, diversification occurs when phenotype distributions become multimodal, with the different modes corresponding to phenotypic clusters, or to species in sexual models. Such pattern formation occurs in partial differential equation models for competitive as well as for predator–prey interactions.

XIII.—Partial Differential Equations and the Calculus of Variations

1927 ◽  
Vol 46 ◽  
pp. 126-135 ◽  
Author(s):  
E. T. Copson
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Calculus Of Variations ◽  
Order Equation ◽  
Second Order ◽  
Physical Problem ◽  
Partial Differential ◽  
Hamiltonian Principle

A partial differential equation of physics may be defined as a linear second-order equation which is derivable from a Hamiltonian Principle by means of the methods of the Calculus of Variations. This principle states that the actual course of events in a physical problem is such that it gives to a certain integral a stationary value.

III. On the differential equations of dynamics. A sequel to a paper on simultaneous differential equations

1863 ◽  
Vol 12 ◽  
pp. 420-424
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Dynamical Problem ◽  
General Character ◽  
Partial Differential ◽  
Central Function ◽  
First Order ◽  
Linear Partial Differential Equations

Jacobi in a posthumous memoir, which has only this year appeared, has developed two remarkable methods (agreeing in their general character, but differing in details) of solving non-linear partial differential equations of the first order, and has applied them in connexion with that theory of the differential equations of dynamics which was established by Sir W. R. Hamilton in the 'Philosophical Transactions’ for 1834-35. The knowledge, indeed, that the solution of the equation of a dynamical problem is involved in the discovery of a single central function, defined by a single partial differential equation of the first order, does not appear to have been hitherto (perhaps it will never be) very fruitful in practical results.

scholarly journals Comparison Theorem for Nonlinear Path-Dependent Partial Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Falei Wang
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Comparison Theorem ◽  
Parabolic Partial Differential Equation ◽  
Basic Variable ◽  
Partial Differential ◽  
Fully Nonlinear ◽  
Path Dependent

We introduce a type of fully nonlinear path-dependent (parabolic) partial differential equation (PDE) in which the pathωton an interval [0,t] becomes the basic variable in the place of classical variablest,x∈[0,T]×ℝd. Then we study the comparison theorem of fully nonlinear PPDE and give some of its applications.

GIẢI PHƯƠNG TRÌNH ĐẠO HÀM RIÊNG SỬ DỤNG MẠNG NEURAL NHÂN TẠO

2020 ◽  
Vol 45 (03) ◽  
Author(s):  
HO DAC QUAN ◽  
HUYNH TRUNG HIEU
Keyword(s):  
Neural Network ◽  
Differential Equation ◽  
Neural Networks ◽  
Partial Differential Equation ◽  
Partial Differential ◽  
Neural Network Method ◽  
Network Method ◽  
Hidden Layer

Phương trình đạo hàm riêng đã được ứng dụng rộng rãi trong các lĩnh vực khác nhau của đời sống như vật lý, hóa học, kinh tế, xử lý ảnh vv. Trong bài báo này chúng tôi trình bày một phương pháp giải phương trình đạo hàm riêng (partial differential equation - PDE) thoả điều kiện biên Dirichlete sửdụng mạng neural truyền thẳng một lớp ẩn (single-hidden layer feedfordward neural networks - SLFN) gọi là phương pháp mạng neural (neural network method – NNM). Các tham số của mạng neural được xác định dựa trên thuật toán huấn luyện mạng lan truyền ngược (backpropagation - BP). Kết quả nghiệm PDE thu được bằng phương pháp NNM chính xác hơn so với nghiệm PDE giải bằng phương pháp sai phân hữu hạn.

scholarly journals Invariant measures for the flow of a first order partial differential equation

1985 ◽  
Vol 5 (3) ◽  
pp. 437-443 ◽  
Author(s):  
R. Rudnicki
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Dynamical Systems ◽  
Differential Equations ◽  
Invariant Measures ◽  
Order Partial Differential Equation ◽  
Partial Differential ◽  
First Order

AbstractWe prove that the dynamical systems generated by first order partial differential equations are K-flows and chaotic in the sense of Auslander & Yorke.

scholarly journals On Exact Solutions of Phi-4 Partial Differential Equation Using the Enhanced Modified Simple Equation Method

2018 ◽  
Vol 6 (4) ◽  
Author(s):  
Ziad Salem Rached
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Simple Equation ◽  
Equation Method ◽  
Partial Differential ◽  
New Exact Solutions ◽  
Modified Simple Equation Method

Constructing exact solutions of nonlinear ordinary and partial differential equations is an important topic in various disciplines such as Mathematics, Physics, Engineering, Biology, Astronomy, Chemistry,… since many problems and experiments can be modeled using these equations. Various methods are available in the literature to obtain explicit exact solutions. In this correspondence, the enhanced modified simple equation method (EMSEM) is applied to the Phi-4 partial differential equation. New exact solutions are obtained.

scholarly journals Memoir on the integration of partial differential equations of the second order in three independent variables, when an intermediary integral does not exist in general

1898 ◽  
Vol 62 (379-387) ◽  
pp. 283-285
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
General Feature ◽  
Partial Differential ◽  
First Order ◽  
Independent Variables ◽  
Dependent Variables ◽  
Two Independent Variables

The general feature of most of the methods of integration of any partial differential equation is the construction of an appropriate subsidiary system and the establishment of the proper relations between integrals of this system and the solution of the original equation. Methods, which in this sense may be called complete, are possessed for partial differential equations of the first order in one dependent variable and any number of independent variables; for certain classes of equations of the first order in two independent variables and a number of dependent variables; and for equations of the second (and higher) orders in one dependent and two independent variables.

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