numerical solution of partial differential equation pdf

... Delay-differential equations In this thesis we are concerned with the numerical solution of delay-differential equations (ĐÉs) Delay-differential equations may best be regarded as extensions of ... the propagation of derivative discontinuities through systems of equations is presented Following a short resumd of standard techniques for the solution of ordinary differential equations (ODÉs), ... University ofManchester for the degree of Doctor of Philosophy in the Faculty of Science. October 1989 Trang 21.1.3 the propagation of derivative discontinuitiesthrough systems of delay-differential equations

Ngày tải lên: 11/10/2014, 04:02

... '',qci The Numerical Solution of Delay-differential Equations by David Richard Wile Department of Mathematics University of Manchester volume II of II A thesis submitted to the University of Manchester ... appendix we give a formal proof of the result (1.1.3:14). For any given time let the order of continuity of the component y i be Z i . Our task is thus to obtain a set of lower bounds {c i : > ... closure of E. Heuristically, by an extension of the above arguments, we may think of Ei as defining the set of points whose continuity bounds can affect the continuity bound, c i , of y i .

Ngày tải lên: 11/10/2014, 04:03

... FOR NUMERICAL SOLUTION OF FOR NUMERICAL SOLUTION OF THE mGRLW EQUATION THE mGRLW EQUATION THE mGRLW EQUATION Nguyen Van Tuan Hanoi Metropolitan University Abstract: In this paper, numerical ... B-spline for numerical solution of the modified equal width wave equation”, J Appl Math Inform., Vol 28(3 - 4), pp 611–624 10 A G Kaplan, Y Dereli (2017), “Numerical solutions of the GEW equation ... EXAMPLE We now obtain the numerical solution of the mGRLW equation for some problems To show the efficiency of the present method for our problem in comparison with the exact solution, we report Lp

Ngày tải lên: 13/01/2020, 09:24

... Therefore, the linearized numerical scheme for the MRLW equation is unconditionally  stable.  4 NUMERICAL EXAMPLE We now obtain the numerical solution of the MRLW equation for some problems. To  ... where U is numerical solution and u denotes exact solution.  Trang 6I = udx, I = (u + βu )dx, I   We have the exact solution of the MRLW is:  cosh (ρ(x − x − ct)),  The initial condition of Equation (1) given by:  ... FOR NUMERICAL SOLUTION OF THE MRLW EQUATION Nguyen Van Dung 1 , Nguyen Viet Chinh 2 1 Hanoi National University of Education 2 Hanoi Metropolitan University Abstract: In this paper, numerical

Ngày tải lên: 28/06/2021, 19:39

... Trang 1IMM DEPARTMENT OF MATHEMATICAL MODELLINGTechnical University of Denmark DK-2800 Lyngby – Denmark May 6, 1999 CBE Numerical Solution of Differential Algebraic Equations Editors: Claus ... Trang 9CHAPTER 1Introduction The (modern) theory of numerical solution of ordinary differential equations(ODEs) has been developed since the early part of this century – beginning withAdams, Runge ... The Van der Pol equation A very famous test problem for systems of ODEs is the Van der Pol equationdefined by the second order differential equation y00 µ 1 y2 y0 y Trang 14This equation may be

Ngày tải lên: 21/12/2016, 10:52

... deflection of the symmetric rectangular support As said in the end of the previous subsection, for the problem of bending of the plate gi = 0 (i = 0, 3) We perform numerical experiments for plate of ... reduction of the order of the equation from four to two. In this study, the method is developed for plates on internal supports of more complex configu-rations Namely, we examine the cases of symmetric ... dual series equations, which then by the Hankel transformation are reduced to the form of a Fredholm integral equation It should be noted that the kernel and the right-hand side of the equation

Ngày tải lên: 26/03/2020, 02:04

... nontrivial solution in the form u(t,r) = v(t)ω(r) Let us consider the integral equation u(t,r) = ∞ h2... nontrivial solution ω(r) ∈ L2 ([0,1)) 3 Proof of Theorem 1.1 3.1 Local existence of nontrivial ... (for the proof see Lemma A.1 in the appendix of this paper) Therefore (1 ) has unique nontrivial solution in the set M Let u be the solution from Theorem 4.1, that is, u is a solution to ... t →0 L2 ([0,∞)) = ∞ (3.62) Svetlin Georgiev Georgiev 23 4 Proof of Theorem 1.2 4.1 Local existence of nontrivial solutions of nonhomogeneous Cauchy problem (1), (2) In this section we

Ngày tải lên: 22/06/2014, 19:20

... more accurate solutions • The size of the integration interval also influences the accuracy of the solutions (should be less than 10% of the time constant) • Solutions of sets of 1st order ODEs ... 21General form of ODE solution methods• New value = old value + integration interval × function of gradient • This is the basis for a family of algorithms used to provide numerical solutions of ODEs ... Trang 1NUMERICAL SOLUTIONSOF ORDINARY DIFFERENTIAL EQUATIONS Trang 2ODEs in Chemical Engineering• The ODEs that occur in Chemical Engineering tend to be of the following form:

Ngày tải lên: 19/03/2015, 08:49

... matter Functional differential equations with state-dependent delay appear frequently in applications as models of equations and for this reason the study of this type of equations has received ... related to partial functional differential equations with state-dependent delay is limited, to our knowledge, to the recent works [21,22] The study of impulsive partial functional differential equations ... boundedness of solutions of impulsive reaction-diffusion equations Positive solutions of nonlinear problems, J Comput Appl Math 88 (1), 175-184, (1998) 7 J.H Liu, Nonlinear impulsive evolution equations,

Ngày tải lên: 29/10/2015, 14:19

... 1UNIVERSITY OF CALIFORNIASanta Barbara Stochastic Partial Differential Equation Models for Highway Traffic A Dissertation submitted in partial satisfaction of the requirement for the degree of Doctor of ... version of systems like(1.3.8) We introduce a multi-lane model that includes the dynamics of lane shifting It is a system of equations, one for each lane The dynamics are determined by an equation of ... (1.3.2) In the context of highway traffic, this step it is not as easy to justify as it is in fluid dynamics, where the ratio of the size of the particles to the size of thedomain of interest is a

Ngày tải lên: 23/05/2017, 22:15

... uniqueness of solutions of differential equations (14) and (15), the map Q m is bijective between two set of solutions of equations (14) and (15) Lemma 2.5 I f all solu tio n s o f the differential equations ... on the existence and uniqueness of solutions (see e.g 1 p 187-189]) An interesting problem studied in the qualitative theory of solutions of ordinary differential equations is to find conditions ... study the asymt.ofcic equivalence of a class of differential equations i l l the Hilbert space H We will establish conditions for which the st udy of the asymptotic equivalence of (1) and (1)

Ngày tải lên: 14/12/2017, 19:52

... years of progress in partial differential equations, and the effect of these 20 years has been so profound that the thinking in the field will never be the same again Perhaps the field of partial ... principle part of an equation or system of equations is nonlinear, a knowledge of characteristics (even their existence) depends on a knowledge of solutions (and their existence) Relative to solutions ... picturization of the D’Alembert solution of the Cauchy problem as given in Section 1 and our exposition of the theory of characteristics Of course, we have not proven existence and uniqueness of solutions

Ngày tải lên: 04/03/2019, 10:36

... Simplicity of Eigenvalues of Robin’s Problem 946.7 Generic Simplicity of Solutions of
u + f (u, x) = 0 in , 7.6 Calculation of some boundary Operators 141 8 The Method of Rapidly-Oscillating Solutions ... Trang 3Perturbation of the Boundary in Boundary-Value Problemsof Partial Differential Equations Trang 5Managing Editor: Professor N J Hitchin, Mathematical Institute,University of Oxford, 24-29 ... Simplicity of Solutions of a System 168 Appendix 1 Eigenvalues of the Laplacian in the Presence Appendix 2 On Micheletti’s Metric Space 188 Trang 11Perturbation of the boundary (or of the domain of definition

Ngày tải lên: 04/03/2019, 11:09

... case of one term, the problems of the existence and uniqueness of solution to (1) in the space C[t0,T ]are studied in detail in [1] In the case of several terms, elements of the theory of corresponding ... the numerical procedures used to solve the classical first kind Volterra equations The reader is referred to [1] for the theory and numerical methods for solving this equation A numerical solution ... inevitable replacement of a large number of generating capacities In this regard, the problem of technical reequipment and dismantling of the main equipment of power plants is one of the most urgent

Ngày tải lên: 12/02/2020, 18:26

... connections of systems of partial differential equations and stochastic differential equations Nicholas A Baran1, George Yin1*and Chao Zhu2 * Correspondence: gyin@math.wayne.edu 1 Department of Mathematics, ... such as smooth dependence of the initial data, recurrence, positive recurrence, ergodicity, stability, and numerical methods for solution of stochastic differential equations with switching, etc., ... to the study of weakly coupled elliptic systems of partial differen-tial equations (see [] for weakly coupled systems) Such systems arise in financial math-ematics and in the form of the so called

Ngày tải lên: 04/12/2022, 10:35

... a solution of the functional equation1.6 In the present paper we investigate the general solution and the generalized Hyers-Ulam-Rassias stability of the functional equation1.6 2 General Solution ... its solutions Thus, it has been called quadratic functional equation, and each of its solutions is said to be a quadratic function Hyers-Ulam-Rassias stability for the quadratic functional equation1.3 ... properly cited 1 Introduction The stability problem of functional equations originated from a question of Ulam1 in 1940, concerning the stability of group homomorphisms LetG1, · be a group, and

Ngày tải lên: 21/06/2014, 20:20

... 2.6 ) admits a global solution. Proof Let ρ be a solution of (2.6) Thenρ ∈ ᐄ(P), the family of all solutions emanating u 1=max where u denotes the usual sup-norm ofu on [0, T] On the other ... paper as “the nature of the vec-tor field.” Therefore, a combination of properties of the associated vector field with theKneser’s property of the cross sections of the solutions’ funnel is the ... proposition, there is a solution ρ ∈ ᐄ(P) that solves the Taking into account the classical theorem of the extendability of solutions, we imposeone more condition on the desired solution lim Trang

Ngày tải lên: 22/06/2014, 22:20

... functions The modeling of some real world problems by using differential equations is a warm area of research in last many years Here we, remark that partial differential equations have important ... the attention of many researches The mentioned tech-niques provide highly accurate numerical solutions to both linear and nonlinear ordinary as well as partial differential equations of classical ... in the application of differential equations in mechanical engineering problems Math Probl Eng 2018; 2018, Article ID 1584920, 3 pages. [11] Ming CY Solution of differential equations with applications

Ngày tải lên: 27/09/2020, 15:23

... of first-order partial differential equations, including questions such as estimates of solutions of initial problems, estimates of domains of solutions, estimates of the difference between solutions ... for functions of several variables by means of functions of one variable which are solutions of ordinary differential equations or inequalities It is shown that there are solutions of initial problems ... 2functions of one variable, which are solutions of ordinary differential equations orinequalities There exist many generalizations of the above classical results We list some of them below Differential

Ngày tải lên: 21/06/2014, 02:20

... p2 = R2=||u||. Then, Equation 7 holds Therefore, by Equations 4 and 7 and the second part of Lemma 2.3, T has a fixed point inP ∩ ( ¯ 2\ 1), which is a positive solution of Equation 1 □ Example ... R2=||u||. Trang 8Then, Equation 12 holds.Therefore, by Equations 10 and 12 and the first part of Lemma 2.3, T has a fixed point inP ∩ ( ¯ 2\ 1), which is a positive solution of Equation 1 □ Example ... subinterval of (0, 1) and satisfies 0< 1−θ θ G(t, s)h(s)ds < +∞. Obviously, uÎ C2 (0, 1) is a solution of Equation 1 if and only if uÎ C(0, 1) satisfies the following nonlinear integral equation

Ngày tải lên: 21/06/2014, 02:20