Boundary value problem

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. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions.

1. What is the difference between IVP and BVP?
2. What is initial and boundary value problems?
3. What is a boundary value problem in elasticity and why is it called that?
4. What is meant by boundary values?

What is the difference between IVP and BVP?

We can solve the system of four first order ordinary differential equations (10.17) to (10.20) as an initial value problem (IVP), where all four boundary conditions are given at one point, or as a boundary value problem (BVP), where four boundary conditions are specified at two distinct points.

What is initial and boundary value problems?

From a mathematical perspective, an initial boundary value problem (IBVP) is called well posed when it has a unique solution that depends continuously on the initial data and the boundary data. The idea for this definition should be clear.

What is a boundary value problem in elasticity and why is it called that?

These boundary conditions and generally comprise given data about the displacements and applied tractions on the surface of the body. The combination of domain equations and boundary conditions is called a boundary value problem.

What is meant by boundary values?

The boundary value is the minimum (or maximum) value that is at the boundary. The number 0 is the maximum number in the first partition, the number 1 is the minimum value in the second partition, both are boundary values.