The monotone method for first-order problems with linear and nonlinear boundary conditions

1994 ◽  
Vol 63 (2-3) ◽  
pp. 163-186 ◽  
Author(s):  
Alberto Cabada
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Monotone Method ◽  
First Order ◽  
Linear And Nonlinear

scholarly journals Accommodating Linear and Nonlinear Boundary Conditions in Wave Digital Simulations of PDE Systems

1997 ◽  
Vol 07 (06) ◽  
pp. 563-597 ◽  
Author(s):  
Cathy Qun Xu ◽  
Steven C. Bass ◽  
Xiaoming Wang
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Digital Simulation ◽  
Nonlinear Boundary Conditions ◽  
Necessary Condition ◽  
Pde Systems ◽  
Discretization Technique ◽  
Linear And Nonlinear ◽  
Digital Simulations ◽  
General Method

The Wave Digital multidimensional discretization technique, recently proposed by A. Fettweis et al., is a potentially important new method for simulating systems of partial differential equations (PDEs), especially those that model processes appearing in nature. To date, no general method has appeared in the literature indicating how to accommodate boundary conditions in Wave Digital simulations. Since the incorporation of a consistent set of boundary conditions within a given PDE system is a necessary condition for that system even to possess a unique solution, it is clear that accounting for boundary conditions within numeric simulations is just as necessary. We present here a method for accommodating lumped, linear or nonlinear boundary conditions into the Wave Digital simulation of either linear or nonlinear PDE systems. Graphic results from the Wave Digital simulation of a simple acoustics problem are also given.

scholarly journals NONLINEAR TRANSVERSE VIBRATIONS OF COMPOSITE RODS UNDER THE ACTION OF A STATICALLY APPLIED TRANSVERSE LOAD

2021 ◽  
Vol 4 (2) ◽  
pp. 29-37
Author(s):  
A. Balamirzoev ◽  
M. Murtuzov ◽  
D. Selimhanov ◽  
Z. Dibirova ◽  
A. Abdullaev
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Transverse Load ◽  
Forced Oscillations ◽  
High Rise ◽  
Composite Rod ◽  
Transverse Vibrations ◽  
Linear And Nonlinear

Nonlinear transverse vibrations of composite rods pre-loaded with lagging arranged symmetrically on both sides of the axis of the composite rod under the action of a statically applied transverse load are investigat-ed. The cases of attaching the lagging only to the ends of the composite rod, as well as when the laggings are continuously attached to the composite rod along its entire length, are considered. The results of the study of nonlinear transverse vibrations of composite rods under the action of a statically applied transverse load are presented. When conducting studies of transverse vibrations of composite rods, solutions of differential equations of vibration of prestressed through beams and stiffening cores of high-rise buildings are obtained. The obtained differential equations of vibration of composite rods allow us to determine the dynamic char-acteristics of prestressed through beams under various linear and boundary conditions. A method for com-posing differential equations of free and forced oscillations of prestressed through beams and stiffening cores of high-rise buildings and solving differential equations under various linear and nonlinear boundary conditions is developed. Expressions are given for determining the longitudinal forces and torques at the ends of the rod at any lo-cation of the lagging from the axis and at any different stiffness of the lagging

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