
1168 SEPARATION OF VARIABLES AND INTEGRAL TRANSFORM METHODS
Originalproblem =
partialdifferentialequationfor
initialconditionsandboundaryconditions,
w w xt= ( , ),
{
ApplicationoftheLaplacetransform 13.6.1.1)(
withrespectto t
Solutionoftheordinarydifferentialequation
withtheboundaryconditions
Applicationoftheinverse
Laplacetransform 13.6.1.2)(
{
Problemfor transform =
ordinarydifferentialequation
for boundaryconditionsw w xp= ( , ),
~~
~~
Findingthetransform w w xp= ( , )
Obtainingsolutiontotheoriginalproblem: w w xt= ( , )
Figure 15.2: Solution procedure for linear boundary value problems using the Laplace
transfo