Results 121 to 130 of about 180 (151)

Strong scheme for a stochastic Goursat problem

Applied Mathematics and Computation, 2004
The authors construct a strong scheme for a stochastic Goursat problem and prove the mean-square convergence to its solution for the approximation generated by the strong scheme. Moreover, they obtain the rate of convergence for the strong scheme.
Shu-Shiang Huang, Yenkun Huang, Che-Yuan Tsai   +2 more
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Uniqueness and Goursat problems

Annali di Matematica Pura ed Applicata, 1969
A uniqueness theorem by W. Walter for a second order Goursat problem in to independent variables is generalized. In the resulting theorem there are no restrictions on the order or on the number of indipendent variables.
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UNIQUENESS CLASSES FOR THE SOLUTION OF GOURSAT'S PROBLEM

Mathematics of the USSR-Izvestiya, 1974
Uniqueness classes for the solution of Goursat's problem, which consists in giving Cauchy initial conditions for each of the variables , , are studied for linear partial differential equations with constant coefficients with two groups of variables: time and space .
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ON PROBLEMS REDUCING TO THE GOURSAT PROBLEM FOR A FOURTH ORDER EQUATION

2007
In this paper, we investigate some problems which can be reduced to the Goursat problem for a fourth order equation. Some results and theorems are given concerning the existence and uniqence for the solution of the suggested problem. ©Shiraz University.
Maher A., Utkina A.
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ON PROBLEMS REDUCED TO THE GOURSAT PROBLEM FOR A THIRD ORDER EQUATION

2006
The aim of the present paper is the investigation of some problems which can be reduced to the Goursat problem for a third order equation. Some results and theorems are given concerning the existence and uniqunce for solving the suggested problem. © Shiraz University.
Maher A., Utkina Y.
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The Goursat and Cauchy Problems for the Sine-Gordon Equation

SIAM Journal on Applied Mathematics, 1978
The equivalence of the methods for solving both the Goursat problem and the Cauchy problem for the sine-Gordon equation is discussed. Sufficient conditions on the initial data for which each problem may be solved by the inverse scattering transform are given. It is shown that the inversion procedure for the Goursat problem is slightly more general than
Kaup, David J., Newell, Alan C.
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On the numerical solution of the Goursat problem

Applied Mathematics and Computation, 1993
The author suggests approximating the Goursat problem, \(u_{xy} = f(x,y,u,u_ x,u_ y)\), by the trapezoidal formula using the harmonic mean for the right hand side. He claims that this gives better results than using the arithmetic or geometric means. His printed results do not appear to support this claim.
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On singular problems of Goursat and Cauchy

Ukrainian Mathematical Journal, 1969
Introduction. In this paper the problems of Goursat and Cauchy are investigated for equations of hyperbolic type with singular coefficients. Effective algorithms are presented for constructing Duhamel functions of such singular initial problems, reducing these problems to a recurrent sequence of ordinary linear nonhomogeneous differential equations of ...
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On Goursat and Dirichlet problems for one equation of the third order

Nonlinear Oscillations, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dzhuraev, T. D., Zikirov, O. S.
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The Goursat problem for Maxwell’s equations

Journal of Mathematical Physics, 1990
Using the spinor formalism of electromagnetism, the Goursat problem for Maxell’s equations is defined and some examples of solutions are given.
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