![]() Then, as superposition preserves the differential equation and the homogeneous side conditions, we will try to build up a solution from these building blocks to solve the nonhomogeneous initial condition \(u(x,0)=f(x)\). Often simplifying assumptions need to be made the challenge is to simplify the equations so that they can be solved but so that they still describe the real-world system well.\), and the homogeneous side conditions, \(u(0,t)=0\) and \(u(L,t)=0\). Section 4.5: The Superposition Principle and Undetermined Coe cients Revisited The Superposition Principle
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