finite difference method when applied to linear second boundary value problem in ordinary differential equation produce a system of linear equation ay=b what is the structure of the coefficient matrix A
Answers
Answer:What is the finite difference method?
The finite difference method is used to solve ordinary differential equations that have
conditions imposed on the boundary rather than at the initial point. These problems are
called boundary-value problems. In this chapter, we solve second-order ordinary differential
equations of the form
f x y y a x b
dx
d y = ( , , '), ≤ ≤ 2
2
, (1)
with boundary conditions
a y(a) = y and b y(b) = y (2)
Many academics refer to boundary value problems as position-dependent and initial value
problems as time-dependent. That is not necessarily the case as illustrated by the following
examples.
The differential equation that governs the deflection y of a simply supported beam under
uniformly distributed load (Figure 1) is given by
EI
qx L x
dx
d y
2
( )
2
2 − = (3)
where
x = location along the beam (in)
E = Young’s modulus of elasticity of the beam (psi)
I = second moment of area (in4
)
q = uniform loading intensity (lb/in)
L = length of beam (in)
The conditions imposed to solve the differential equation are
y(x = 0) = 0 (4)
y(x = L) = 0
Clearly, these are boundary values and hence the problem is considered a boundary-value
problem.
Step-by-step explanation: