NUMERICAL METHOD OF LINES FOR FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS WITH DEVIATED VARIABLES

AbstractSpatial motion of an ideal inextensible thread is described by six first order partial differential equations with one space variable and one algebraic equation that has to be valid at each point. In the paper, new formulation of the problem without an algebraic equation is suggested. It is proved that the new problem is equivalent to the original one and an efficient numerical method for its solution is developed.

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Formation of Shocks for Nonlinear Partial Differential Equations of First Order

Proceedings of the Fourth International Colloquium on Differential Equations, Plovdiv, Bulgaria, 18–22 August 1993 ◽

10.1515/9783112318874-022 ◽

1994 ◽

pp. 199-204

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Nonlinear Partial Differential Equations ◽

Partial Differential ◽

First Order

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Block-pulse series solution of simultaneous first-order partial differential equations

International Journal of Systems Science ◽

10.1080/00207728508926776 ◽

1985 ◽

Vol 16 (12) ◽

pp. 1573-1580 ◽

Cited By ~ 1

Author(s):

MING-HWEI PERNG ◽

WEN-LIANG CHEN

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Series Solution ◽

Partial Differential ◽

First Order

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Pathwise convergence of a numerical method for stochastic partial differential equations with correlated noise and local Lipschitz condition

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2017.04.012 ◽

2017 ◽

Vol 323 ◽

pp. 123-135 ◽

Cited By ~ 1

Author(s):

Minoo Kamrani ◽

Dirk Blömker

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Numerical Method ◽

Lipschitz Condition ◽

Stochastic Partial Differential Equations ◽

Correlated Noise ◽

Partial Differential ◽

Local Lipschitz Condition

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Entire solutions of first-order nonlinear partial differential equations

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-97-03881-1 ◽

1997 ◽

Vol 125 (5) ◽

pp. 1483-1485 ◽

Cited By ~ 14

Author(s):

Jill E. Hemmati

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Nonlinear Partial Differential Equations ◽

Entire Solutions ◽

Partial Differential ◽

First Order

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Div First-Order System LL* (FOSLL*) for Second-Order Elliptic Partial Differential Equations

SIAM Journal on Numerical Analysis ◽

10.1137/140971890 ◽

2015 ◽

Vol 53 (1) ◽

pp. 405-420 ◽

Cited By ~ 3

Author(s):

Zhiqiang Cai ◽

Rob Falgout ◽

Shun Zhang

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Elliptic Partial Differential Equations ◽

Second Order ◽

Order System ◽

Partial Differential ◽

First Order

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A Difference Method for Plane Problems in Magnetoelastodynamics

Journal of Applied Mechanics ◽

10.1115/1.3422774 ◽

1972 ◽

Vol 39 (3) ◽

pp. 689-695 ◽

Cited By ~ 4

Author(s):

W. W. Recker

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Numerical Method ◽

Difference Method ◽

Necessary Condition ◽

Two Dimensional ◽

Symmetric Hyperbolic System ◽

Von Neumann ◽

First Order ◽

Independent Variables

The two-dimensional equations of magnetoelastodynamics are considered as a symmetric hyperbolic system of linear first-order partial-differential equations in three independent variables. The characteristic properties of the system are determined and a numerical method for obtaining the solution to mixed initial and boundary-value problems in plane magnetoelastodynamics is presented. Results on the von Neumann necessary condition are presented. Application of the method to a problem which has a known solution provides further numerical evidence of the convergence and stability of the method.

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