Question

Difference between boundary condition and initial condition

Answer 1

*Boundary condition-In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions.


*Initial condition-In mathematics, the field of differential equations, an initial value problem (also called the Cauchy problem by some authors) is an ordinary differential equation together with a specified value, called the initial condition, of the unknown function at a given point in the domain of the solution.

Answer 2

Answer:

A boundary condition expresses how a function behaves at the edge (border) of its defined region. An initial condition is Similar to a boundary condition, but applied to the time-direction.

Explanation:

Two additional criteria apply to a time-space partial differential equation, particularly when the space derivative(s) is (are) of order larger than one:

Initial conditions: These are referred to as initial circumstances, and they always exist at time t0. You require n starting conditions with time derivatives up to order n1 if n is the highest order of the time derivative.

Boundary conditions: The space derivatives are typically ordered in an even fashion. You require n boundary conditions at the boundary of the region where the PDE holds if 2n is the order of the space derivatives. The BCs are capable of holding derivatives of up to order 2n-1.

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