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zheng89120
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What kind of systems do ODEs describe?
What kind of systems do PDEs describe?
What kind of systems do PDEs describe?
ODEs are used in case of a physical phenomena which can be modeled with functions of a variable only.What kind of systems do ODEs describe?
What kind of systems do PDEs describe?
Physically, what is the difference between systems of ODEs and PDEs?
zheng89120 said:What kind of systems do ODEs describe?
What kind of systems do PDEs describe?
The main difference between ODEs (ordinary differential equations) and PDEs (partial differential equations) is the number of independent variables. ODEs have only one independent variable, while PDEs have multiple independent variables.
The solution techniques for ODEs and PDEs also differ due to the number of independent variables. ODEs can be solved using analytical methods such as separation of variables or integration, while PDEs often require numerical methods such as finite difference or finite element methods.
One example of a physical system described by ODEs is the motion of a simple pendulum, while an example of a system described by PDEs is the diffusion of heat in a solid object.
The boundary conditions for ODEs are typically specified at the endpoints of the independent variable, while for PDEs, boundary conditions are specified along the boundaries of the spatial domain.
ODEs and PDEs are used in many fields of science and engineering to model and understand various physical phenomena. Some examples include modeling population dynamics, predicting weather patterns, and simulating fluid flow in pipes or around objects.