Top PDF Elementary Differential Equations with Boundary Value Problems

Elementary Differential Equations with Boundary Value Problems

Elementary Differential Equations with Boundary Value Problems

Traditionally oriented elementary differential equations texts are occasionally criticized as being col- lections of unrelated methods for solving miscellaneous problems. To some extent this is true; after all, no single method applies to all situations. Nevertheless, I believe that one idea can go a long way toward unifying some of the techniques for solving diverse problems: variation of parameters. I use variation of parameters at the earliest opportunity in Section 2.1, to solve the nonhomogeneous linear equation, given a nontrivial solution of the complementary equation. You may find this annoying, since most of us learned that one should use integrating factors for this task, while perhaps mentioning the variation of parameters option in an exercise. However, there’s little difference between the two approaches, since an integrating factor is nothing more than the reciprocal of a nontrivial solution of the complementary equation. The advantage of using variation of parameters here is that it introduces the concept in its simplest form and
Show more

806 Read more

Elementary Differential Equations and Boundary Value Problems. 10th Edition International Student Version

Elementary Differential Equations and Boundary Value Problems. 10th Edition International Student Version

Description: The 10th edition of Elementary Differential Equations and Boundary Value Problems, like its predecessors, is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. The authors have sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and

6 Read more

Elementary Differential Equations with Boundary Value Problems

Elementary Differential Equations with Boundary Value Problems

Traditionally oriented elementary differential equations texts are occasionally criticized as being col- lections of unrelated methods for solving miscellaneous problems. To some extent this is true; after all, no single method applies to all situations. Nevertheless, I believe that one idea can go a long way toward unifying some of the techniques for solving diverse problems: variation of parameters. I use variation of parameters at the earliest opportunity in Section 2.1, to solve the nonhomogeneous linear equation, given a nontrivial solution of the complementary equation. You may find this annoying, since most of us learned that one should use integrating factors for this task, while perhaps mentioning the variation of parameters option in an exercise. However, there’s little difference between the two approaches, since an integrating factor is nothing more than the reciprocal of a nontrivial solution of the complementary equation. The advantage of using variation of parameters here is that it introduces the concept in its simplest form and
Show more

807 Read more

Elementary Differential Equations with Boundary Value Problems

Elementary Differential Equations with Boundary Value Problems

Traditionally oriented elementary differential equations texts are occasionally criticized as being col- lections of unrelated methods for solving miscellaneous problems. To some extent this is true; after all, no single method applies to all situations. Nevertheless, I believe that one idea can go a long way toward unifying some of the techniques for solving diverse problems: variation of parameters. I use variation of parameters at the earliest opportunity in Section 2.1, to solve the nonhomogeneous linear equation, given a nontrivial solution of the complementary equation. You may find this annoying, since most of us learned that one should use integrating factors for this task, while perhaps mentioning the variation of parameters option in an exercise. However, there’s little difference between the two approaches, since an integrating factor is nothing more than the reciprocal of a nontrivial solution of the complementary equation. The advantage of using variation of parameters here is that it introduces the concept in its simplest form and
Show more

807 Read more

Elementary Differential Equations and Boundary Value Problems

Elementary Differential Equations and Boundary Value Problems

In each of Problems 34 through 37 use the method of Problem 33 to find a second independent solution of the given equation. 34[r]

806 Read more

Boundary value problems for fractional differential equations

Boundary value problems for fractional differential equations

where  < α ≤  is a real number, D α  + is the Riemann-Liouville fractional differential op- erator of order α. By means of fixed point theorems, they obtained results on the existence of positive solutions for BVPs of fractional differential equations. In [], Bai considered the boundary value problem of the fractional order differential equation

11 Read more

Boundary value problems for stochastic differential equations

Boundary value problems for stochastic differential equations

BOUNDARY VALUE PROBLEHS FOR STOCHASTIC DIFFERENTIAL EQUATIONS Thesis by Thomas 1 Tilliam HacDm rell In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy California Institu[.]

86 Read more

Singular boundary value problems for quasi differential equations

Singular boundary value problems for quasi differential equations

diffusion problems, Appl. Existence theorems for certain classes of singular boundary value problems, J. Existence theorens for a singular two-point Dirichlet problem, Nonlin. Existence [r]

8 Read more

Boundary value problems for differential equations with reflection of the argument

Boundary value problems for differential equations with reflection of the argument

Differential equations with involutions can be transformed by differen- tiation to higher order ordinary differential equations and, hence, admit of point data initial or boundary condit[r]

13 Read more

Boundary value problems for fractional differential equations with nonlocal boundary conditions

Boundary value problems for fractional differential equations with nonlocal boundary conditions

Abstract In this paper, we establish some sufficient conditions for the existence of solutions to two classes of boundary value problems for fractional differential equations with nonlocal boundary conditions. Our goal is to establish some criteria of existence for the boundary problems with nonlocal boundary condition involving the Caputo fractional derivative, using Banach’s fixed point theorem and Schaefer’s fixed point theorem. Finally, we present four examples to show the importance of these results.

12 Read more

The numerical solution of boundary value problems in partial differential equations

The numerical solution of boundary value problems in partial differential equations

in the difference solution were sho?n to oe dependent on the pov.ors 01 thia aatr'x, and, therefore, to grow with the number of time steps* In chapte: 1 it was pointed out that a spectral radius of this order would give hounded errors In a closed region, 0 < t < T, but that the errors would become unbounded as t -» <*• Thus, problems of numerical instability in the solution of the third boundary value probl«a for the heat equation, which ari^e from the boundary conditions, arc important only for large values of the time. However, this type of instability aastnes a new
Show more

157 Read more

Boundary value problems for hybrid differential equations with fractional order

Boundary value problems for hybrid differential equations with fractional order

d dt [ f (t,x(t)) x(t) ] = g(t, x(t)) a.e. t ∈ J = [,T ], x(t  ) = x  ∈ R, where f ∈ C(J × R, R\{}) and g ∈ C(J × R, R). They established the existence, uniqueness results and some fundamental differential inequalities for hybrid differential equations ini- tiating the study of theory of such systems and proved utilizing the theory of inequalities, its existence of extremal solutions and comparison results.

19 Read more

Some results on boundary value problems for functional differential equations

Some results on boundary value problems for functional differential equations

The purpose of this paper is t() provide existen(’e results fi)r second ()r(h’r t)omdary value problems (BVP fi)r short) fi)r flm(’tional differential (,qmtions.. Tt,’s, cmditims. fiw th[r]

8 Read more

Existence of solutions of boundary value problems for functional differential equations

Existence of solutions of boundary value problems for functional differential equations

Analogous boundal.y value pPoblems fop oPdinary differential equations has been studied by many authors, who used the Leray-Schauder continuation theorem (see Lasota and Yorke [I], Szman[r]

8 Read more

Solvability of boundary value problems of nonlinear fractional differential equations

Solvability of boundary value problems of nonlinear fractional differential equations

1 Introduction Fractional differential equations have been of great interest. It is caused both by the in- tensive development of the theory of fractional calculus itself and by the applications. Apart from diverse areas of mathematics, fractional differential equations arise in rhe- ology, dynamical processes in self-similar and porous structures, fluid flows, electrical networks, viscoelasticity, chemical physics, and many other branches of science; see [–

13 Read more

General boundary value problems for pseudo differential equations and related difference equations

General boundary value problems for pseudo differential equations and related difference equations

It is well known that the term ‘elliptic boundary value problem’ means not only satisfying certain equation in inner points of a manifold, but satisfying some boundary conditions as well. But it is not enough. These boundary conditions have been assiciated with inner equation, and these conditions of concordance are called Shapiro-Lopatinskii conditions.

7 Read more

Existence of solution for integral boundary value problems of fractional differential equations

Existence of solution for integral boundary value problems of fractional differential equations

Abstract In this paper, we discuss the existence of positive solutions of fractional differential equations on the infinite interval (0, +∞). The positive solution of fractional differential equations is gained by using the properties of the Green’s function, Leray–Schauder’s fixed point theorems, and Guo–Krasnosel’skii’s fixed point theorem.

13 Read more

Existence of Solutions for Boundary Value Problems of Conformable Fractional Differential Equations

Existence of Solutions for Boundary Value Problems of Conformable Fractional Differential Equations

In this paper, we study a class of boundary value problems for conformable fractional differential equations under a new definition. Firstly, by using the monotone iterative technique and the method of coupled upper and lower solution, the sufficient condition for the existence of the boundary value problem is obtained, and the range of the solution is determined. Then the existence and uniqueness of the solution are proved by the proof by contra- diction. Finally, a concrete example is given to illustrate the wide applicability of our main results.
Show more

10 Read more

Periodic Boundary Value Problems for Second Order Functional Differential Equations

Periodic Boundary Value Problems for Second Order Functional Differential Equations

Upper and lower solution method plays an important role in studying boundary value problems for nonlinear differential equations; see 1 and the references therein. Recently, many authors are devoted to extend its applications to boundary value problems of functional differential equations 2–5. Suppose α is one upper solution or lower solution of periodic boundary value problems for second-order differential equation; the condition α0 αT is required. A neutral problem is that whether we can define upper and lower solution without assuming α0 αT. The aim of the present paper is to discuss the following second order functional differential equation
Show more

11 Read more

Boundary value problems for partial differential equations with piecewise contant delay

Boundary value problems for partial differential equations with piecewise contant delay

Partial Differential Equation, Piecewise Con- stant Delay, Boundary Value Problem, Fourier Method, Positive Opera-.. tor, Weak Solution.[r]

17 Read more

Show all 10000 documents...