Boundary and initial conditions

boundary conditions are essential to obtain a solution of a boundary value problem, Boundary conditions are defined at the boundary of an independent variable in an equation whereas in initial value condition has all of the condition defined at the same value of the independent variable in an equation.

for example, boundary conditions are like at t =0 and t = 1 we have to calculate the value of function f(t)

in initial value problem would give the value of function f(t) and f\'(t) at time t = 0.

Types of Boundary Conditions:

1.) Dirichlet Condition: - the Dirichlet boundary condition define the value of a function itself on the surface i.e.

y = f(t)

2.) Neumann condition: - the Neumann boundary condition define the value of a normal derivative of a function on the surface.

dy/dn = f(t)