Open AccessBook
Applied partial differential equations
Donald W. Trim
- 01 Jul 1990
TL;DR: In this paper, the main emphasis is placed on techniques for solving partial differential equations found in physics and engineering but discussions on existence and uniqueness of solutions are included Several different methods of solution are presented, with the primary emphasis on the classical method of separation of variables Secondary emphasis was placed on transform solutions, as well as on the method of Green's functions.
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Abstract: The emphasis in this book is placed on techniques for solving partial differential equations found in physics and engineering but discussions on existence and uniqueness of solutions are included Several different methods of solution are presented, with the primary emphasis on the classical method of separation of variables Secondary emphasis is placed on transform solutions, as well as on the method of Green's functions The derivation and analysis of heat, wave and potential equations are covered in chapter one, and throughout the book the physical interpretation of mathematical results is stressed A background of elementary calculus and differential equations is necessary
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Citations
Control of a long-line-type plant
M. Szymkat,H. Gorecki,L. Popek +2 more
TL;DR: In this article, an approach to the feedback loop controller design problem for plants described by linear partial differential equations of a long-line type is presented, where the classical frequency domain technique called "the optimal modulus criterion" is applied.
Robust-to-Change Stiffness Allocation for Tall Structures
TL;DR: In this article, a computational procedure for robust modeling and robust-to-modeling of structural systems is proposed with application to planar rigid frames, where a structure is considered robust when it is least sensitive to changes that alter its system coefficients (stiffness matrix for static loading).
Parabolic Equations: Explicit Method
Daniel Zwillinger
- 01 Jan 1992
TL;DR: In this article, an explicit numerical scheme for parabolic partial differential equations is obtained. But the main drawback of this method is that Δt must often be very small for the method to be stable.
Finite Difference Formulas
Daniel Zwillinger
- 01 Jan 1992
TL;DR: In this article, a table of finite difference formulas for some common grids and common equations can be found, which is applicable to differential equations that will be solved by the method of finite differences.
On second order discontinuous differential equations in Banach spaces
Seppo Heikkilä,S. Leela +1 more
TL;DR: In this paper, the existence of extremal mild solutions of the second-order semilinear near-near-linear value problem (IVP) was studied in an ordered Banach space, where the linear operator in the dfferential equat}on is the nfinitesimal generator of a strongly continuous cos}ne family in a Banachspace.
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