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Applications to Ordinary Differential Equations
1971Publisher Summary The theories of ordinary and partial differential equations are the fruitful sources of integral equations. In the quest for the representation formula for the solution of a linear differential equation in such a manner so as to include the boundary condition or initial condition explicitly, one is always led to an integral equation.
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Ordinary Differential Equations
1996We begin with a general form of the problem that will occupy our attention throughout most of Chapter I. Consider the linear two-point boundary value problem $$ Lu: = - \varepsilon u'' + b\left( x \right)u' + c\left( x \right)u = f\left( x \right)\quad for\quad x \in \left( {d,e} \right), $$ with the boundary conditions $$ \begin{gathered} {\
Lutz Tobiska +2 more
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Ordinary Differential Equations
1989The major purpose of the present chapter is to demonstrate the use of the volume integral method in deriving accurate, stable, and physically realistic difference equations from ordinary differential equations. A secondary purpose is to develop the proper ideas and procedures for later use in deriving difference equations from partial differential ...
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Coupling of FEM and ordinary state-based peridynamics for brittle failure analysis in 3D
Mechanics of Advanced Materials and Structures, 2021Tao Ni, Mirco Zaccariotto, Qi-Zhi
exaly
Ordinary Differential Equations
2019The concept of first integrals of ODEs is introduced. Application is made to Newton’s second law of motion in one dimension.
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Ordinary Differential Equations
1998Let f be a C 1 vector field on an open set U in E . If f(x o ) = 0 for some x o ∈U, if a: J →U is an integral curve for f, and there exists some to ∈J such that α(t o ) = x o , show that α(t) = x o for all t∈J. (A point x o such that f(x 0 )= 0 is called a critical point of the vector field.)
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Model for Simulating Aerosol Interactions and Chemistry (MOSAIC)
Journal of Geophysical Research, 2008Rahul A Zaveri +2 more
exaly