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As the thread title says: What's the difference between initial conditions and boundary conditions?
Thanks in advance for helpful replies. :)
Thanks in advance for helpful replies. :)
Galileo said:There's no difference from a mathematical point of view (As far as I recall).
Actually, there is an important mathematical difference: existence and uniqueness of solutions for intial value problems depends only on the equation. For boundary value value problems, it depends on the equation and the boundary condition.mathwonk said:i would also say no difference at all.
Initial conditions refer to the parameters or values that are set at the beginning of a scientific experiment or simulation. They are the starting point for the system being studied and can greatly influence the outcome of the experiment.
Boundary conditions refer to the limits or constraints that are placed on a system being studied. These can include factors such as temperature, pressure, or other external forces that affect the behavior of the system.
Initial conditions are the starting point for a system, while boundary conditions define the limits or constraints that the system must operate within. Initial conditions can be changed or varied to observe different outcomes, while boundary conditions are typically constant throughout an experiment.
Initial and boundary conditions are important because they help to define and control the parameters of a scientific study. They allow scientists to observe and analyze the behavior of a system under specific conditions, and can help to determine the validity of their hypotheses.
Yes, initial and boundary conditions can change throughout an experiment. This can be done to observe how the system behaves under different conditions or to test the sensitivity of the system to various parameters. However, it is important to carefully document and track any changes to these conditions in order to accurately analyze the results of the experiment.