One Dimensional Heat Flow
In Chapter 1, it was indicated that many phenomena of physics and engineering are expressed by partial differential equations PDEs. The PDE is termed a Boundary Value Problem (BVP) if the boundary conditions of the dependent variable u and some of its partial derivatives are often prescribed. However, the PDE is called an Initial Value Problem (IVP) if the initial conditions of the dependent variable u are prescribed at the starting time t=0. Moreover, the PDE is termed Initial-Boundary Value Problem (IBVP) if both initial conditions and boundary conditions are prescribed.
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- 6.F. John, Partial Differential Equations, Springer-Verlag, New York, (1982)Google Scholar