A COMPLETE EXPRESSION OF THE ASYMPTOTIC SOLUTION OF DIFFERENTIAL EQUATION WITH A∩-TH ORDER TURNING POINT

A second order linear ordinary differential equation has been studied, and the complete expresson, of the formal uniformly valid asymptotic solutions to the equation near turning point is obtained by using extended Airy function.     

THE EXPONENTIAL ASYMPTOTIC SOLUTION OF DIFFERENTIAL EQUATION

In this paper, the exponential asgmptotic solution (E.A.S.) of differential equation is discussed. Firstly, E.A.S. of the second-order differential equation is studied and the orthogonal conditions of the uniformly valid E.A.S. are found out. Next, E.A.S. in matched asymptotic method is discussed. Finally, some examples are given.     

THE ASYMPTOTIC EXPRESSION OF THE SOLUTION OF THE CAUCHY’S PROBLEM FOR A HIGHER ORDER LINEAR ORDINARY DIFFERENTIAL EQUATION WHEN THE LIMIT EQUATION HAS SINGULARITY

ＴＨＥＡＳＹＭＰＴＯＴＩＣＥＸＰＲＥＳＳＩＯＮＯＦＴＨＥＳＯＬＵＴＩＯＮＯＦＴＨＥＣＡＵＣＨＹ’ＳＰＲＯＢＬＥＭＦＯＲＡＨＩＧＨＥＲＯＲＤＥＲＬＩＮＥＡＲＯＲＤＩＮＡＲＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＷＨＥＮＴＨＥＬＩＭＩＴＥＱＵＡＴＩＯＮ...     

PERTURBATION SOLUTION OF THE WEAK-NONLINEAR DIFFERENTIAL EQUATION WITH δ-FUNCTION

In this paper, starting from some fundamental properties of Heaviside function and δ-function, making use of singular perturbation methods we provide a method of finding the asymptotic analytic solution of equation where M is an n -order linear differential operator, f(u) is a polynomial. By means of this method, we discuss some examples concretely. The results can be explained satisfac-torily in physics. If we deal with linear problem by this method, the result will agree with that drawn from theorem of impulse.     

PERTURBATION SOLUTION OF THE WEAK-NONLINEAR PARTIAL DIFFERENTIAL EQUATION WITH δ-FUNCTION

In this paper we extend the method which Liu Zheng-rong provided to the weak-nonlinear partial equation with δ -function.     

PERTURBATION SOLUTION OF THE WEAK-NONLINEAR PARTIAL DIFFERENTIAL EQUATION WITH δ-FUNCTION

In this paper we extend the method which Liu Zheng-rong provided to the weak-nonlinear partial equation with δ-function.     

THE NUMERICAL SOLUTION FOR PROBLEMS OF TURNING POINT WITHOUT RESONANCE

In this paper the uniform convergence of Ⅱin scheme to the turning point problemswithout resonance is proved by means of Kellogg’s method The given estimation is shown tobe optimal.     

INSTABILITY OF SOLUTION FOR THE THIRD ORDER LINEAR DIFFEBENTIAL EQUATION WITH VARIED COEFFICIENT

In reference [1] asymptotic stability of dynamic system with slowly changing coefficients for all characteristic roots which have negative real part has been proved by means of Liapunov's second method. In this paper, we give some sufficient conditions of the instability for the third order linear differential equation with varied coefficient, at least one of the characteristic roots of which has positive real part, by means of Liapunov's second method.     

EXISTENCE OF SOLUTIONS OF THREE－POINT BOUNDARY VALUE PROBLEMS FOR NONLINEAR FOURTH ORDER DIFFERENTIAL EQUATION

ＥＸＩＳＴＥＮＣＥＯＦＳＯＬＵＴＩＯＮＳＯＦＴＨＲＥＥ－ＰＯＩＮＴＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＦＯＲＮＯＮＬＩＮＥＡＲＦＯＵＲＴＨＯＲＤＥＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮ￥ＧａｏＹｏｎｇｘｉｎ（高永馨）（Ｄｅｐａｒｔｍｅｎｔｏ...     

SOLUTIONS OF THE GENERALn－TH ORDER VARIABLE COEFFICIENTS LINEAR DIFFERENCE EQUATION

ＳＯＬＵＴＩＯＮＳＯＦＴＨＥＧＥＮＥＲＡＬｎ－ＴＨＯＲＤＥＲＶＡＲＩＡＢＬＥＣＯＥＦＦＩＣＩＥＮＴＳＬＩＮＥＡＲＤＩＦＦＥＲＥＮＣＥＥＱＵＡＴＩＯＮＺｈｏｕＺｈｉ－ｈｕ（周之虎）（ＡｎｈｕｉＡｒｃｈｉｔｅｃｔｕｒｅＩｎｄｕｓｔｒｙＣｏｌｌｅｇｅ）．Ｈ...     

TO SOLVE THE SHALLOW SHELL EQUATIONS WITH THE HELP OF THE PLATE’S EQUATION SOLUTION(LOWERING THE ORDER OF PARTIAL DIFFERENTIAL EQUATION FROM 8 TO 2)

If a plate solution is known which has the same boundary and loading conditions with ashallow shell,the solution of that shell can be reduced to a non-homogeneous Helmholtz’sequation in complex domain.Two examples are given to illustrate our method.     

NUMERICAL SOLUTION OF QUASILINEAR SINGULARLY PERTURBED ORDINARY DIFFERENTIAL EQUATION WITHOUT TURNING POINTS

In this paper we consider a quasilinear second order ordinary differential equation equation witha small parameter e.Firstly an approximate problem is constructed.Then an iterativeprocedure is developed.Finally we give an algorithm whose accuracy is good for arbitraryε>0.     

TO SOLVE THE SHALLOW SHELL EQUATIONS WITH THE HELP OF THE PLATE’S EQUATION SOLUTION(LOWERING THE ORDER OF PARTIAL DIFFERENTIAL EQUATION FROM 8 TO 2)

If a plate solution is known which has the same boundary and loading conditions with a shallow shell, the solution of that shell can be reduced to a non-homogeneous Helmholtz’s equation in complex domain. Two examples are given to illustrate our method.     

THE EXISTENCE OF PERIODIC SOLUTION OF THE FOURTH ORDINARY NONLINEAR DIFFERENTIAL EQUATION CAUSED BY FLOW－IN

ＴＨＥＥＸＩＳＴＥＮＣＥＯＦＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＯＦＴＨＥＦＯＵＲＴＨＯＲＤＩＮＡＲＹＮＯＮＬＩＮＥＡＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＣＡＵＳＥＤＢＹＦＬＯＷ－ＩＮＤＵＣＥＤＶＩＢＲＡＴＩＯＮＧｕＱｉｎｇ－ｆａｎｇ（顾清芳）Ｔａ...     

THE BOUNDED SOLUTION OF A CLASS OF DIFFERENTIAL-DIFFERENCE EQUATION OF ADVANCED TYPE AND ITS ASYMPTOTIC BEHAVIOR

In this paper, we consider the differential-difference equation of advanced type with perturbation term. It is shown that if the bounded solution of the reduced equation has negative exponential order and the perturbation term f satisfies certain condition, then the bounded solution of the perturbation equation has negative exponential order.     

THE ASYMPTOTIC SOLUTION OF A KIND OF STEFAN PROBLEM

In this paper,a kind of Stefan problem subject to general initial condition is studied.The slab considered is divided into three regions.There is a different time scale in each one.By means of PLK method or like multi-scales method,the asympto-tic solution of each one is obtained.Finally we discuss the asymptotic solution and draw some conclusions.     

THE NUMERICAL SOLUTION OF A SINGULARLY PERTURBED PROBLEM FOR SEMILINEAR PARABOLIC DIFFERENTIAL EQUATION

The numerical solution of a singularly perturbed problem for the semilinear parabolicdifferential equation with parabolic boundary layers is discussed.A nonlinear two-leveldifference scheme is constructed on the special non-uniform grids.The uniform convergenceof this scheme is proved and some numerical examples are given.     

ASYMPTOTIC EXPERSSION OF THE SOLUTION OF GENERAL BOUNDARY VALUE PROBLEN FOR HIGHER ORDER ELLIPTIC EQUATION WITH PERTURBATION BOTH IN BOUNDARY AND IN OPERATOR

In this paper basing on (1) and (2),we study thesingular perturbation of general boundary value problemfor higher order elliptic equation with perturbationboth in the boundary and in the operator,so as to es-tablish the asymptotic expression involving two para-meters.Thus,the iterative process of finding theasymptotic solution is derived and the estimation ofthe remainder term is given out,we extend and improvethe previously published papers.     

MIKUSINSKI＇S OPERATORS SOLUTION OF THREE－ORDER LINEAR DIFFERENCE EQUATION WITH VARIABLE COEFFICIENTS

ＭＩＫＵＳＩＮＳＫＩ＇ＳＯＰＥＲＡＴＯＲＳＳＯＬＵＴＩＯＮＯＦＴＨＲＥＥ－ＯＲＤＥＲＬＩＮＥＡＲＤＩＦＦＥＲＥＮＣＥＥＱＵＡＴＩＯＮＷＩＴＨＶＡＲＩＡＢＬＥＣＯＥＦＦＩＣＩＥＮＴＳＺｈｏｕＺｈｉ－ｈｕ（周之虎）（ＡｎｈｕｉＡｒｃｈｉｔｅｃｔｕｒａｌＩ...     

ON THE SINGULAR PERTURBATION OF A NONLINEAR ORDINARY DIFFERENTIAL EQUATION WITH TWO PARAMETERS

In this paper,the method of differential inequalities has been applied to study theboundary value problems of nonlinear ordinary differential equation with two parameters.The asymptotic solutions have been found and the remainders have been estimated.