# Question:Non-homogeneous Boundary Condition

## Question:Non-homogeneous Boundary Condition

Maple

I am trying to modify a solution to a non-homogeneous boundary value problem presented in Dr. Lopez's Advanced Engineering Mathematics package, Section 27.2, One-Dimensional Heat Equation with Time-Varying Endpoint Temperatures.  The solution steps are detailed for the case of a time varying temperature which is a sinusoidal function; however, the problem I am modeling has a boundary condition which is piecewise continuous.  The varying endpoint temperature is given by a temperature time-history data set which cannot be described with a continuous function, as the example does.  My help request is that for a given set of ordered pairs of temperature vs. time, what is the best way to create a function in Maple that will return the temperature for a given time.  The first few data pairs are given below:

{0, 100}, {0.005, 300}, {3600, 320}, {7200, 320}, {43200, 310} ...

Any suggestions on developing a procedure/function within Maple to establish the time varying endpoint for a piecewise continuous function would be greatly appreciated.  Thank you for your help.

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