Results 251 to 260 of about 55,126 (291)

First-order partial differential equations

2009
In this chapter we will discuss the first order linear partial differential equations, homogeneous and inhomogeneous. Partial differential equations of first order are used to model traffic flow on a crowded road, blood flow through an elastic-walled tube, shock waves and as special cases of the general theories of gas dynamics and hydraulics.
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First Order Partial Differential Equations

1992
A relation, in which the independent variables x 1 x 2, ..., x n , and the unknown function u of these variables together with its first partial derivatives appear is called the first order partial differential equation.
Gheorghe Micula, Paraschiva Pavel
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Semicirculant Preconditioners for First-Order Partial Differential Equations

SIAM Journal on Scientific Computing, 1994
The authors solve a system of \(n\) first-order partial differential equations in two space dimensions of the hyperbolic type. The main considerations concern the steady-state problem, but the results are compared with analogous results given by the second author in his earlier report for the time-dependent case.
Holmgren, Sverker, Otto, Kurt
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First-Order Partial Differential Equations

1990
In this chapter we study the solution of first-order partial differential equations of the ...
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First-Order Partial Differential Equations

1983
Partial differential equations have been studied much less than ordinary differential equations. Part of the theory—that of a single partial differential equation of the first order—can be reduced to the study of special ordinary differential equations, the so-called characteristic equations.
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First Order Stochastic Partial Differential Equations

1984
Publisher Summary This chapter discusses the first order stochastic partial differential equations. The chapter studies the Cauchy problem of the first order stochastic partial differential equations of the parabolic type. The method of stochastic characteristic curve has been proposed to construct a solution of a suitable linear stochastic partial ...
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First-Order Partial Differential Equations

2020
Nita H. Shah, Mrudul Y. Jani
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Partial Differential Equations of the First Order

2020
We consider linear partial differential equations of the first order. A partial differential equation is linear if the dependent variables, i.e., the functions that are being solved for, appear only to the first power and the coefficients, i.e., the factors the derivatives are multiplied by, do not contain the dependent variables.
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First-order Partial Differential Equations

2023
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Partial differential equations of the first-order

2000
Although the major focus of these introductory volumes is on linear partial differential equations of second- and higher-order, it is instructive to examine some aspects of first-order partial differential equations. These can arise in a number of engineering applications including the study of waves in shallow water, traffic flow, gas dynamics ...
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