## Computational methods in distributed parameter systems |

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adjoint equation algorithm based Banach space Boundary Value Problem called boundary control Choose any m^g Compute and Store Crank-Nicholson method delta function differential relations diffusion process directed normal distributed control distributed parameter systems distributed systems dition dynamics eigen function equa equation is solved Equation On reducing error functional explicit method finite differences flow diagram Gateaux derivative Hamiltonian heat equation homogeneous boundary conditions initial choice Initial condition U(x,tQ interior points iterations required known linear operator lumped systems maximum value mg(t minimizes the error mode of oscillation non-quadratic performance index non-quadratic term number of iterations Numerical Solution optimal optimum boundary control optimum solution optimum trajectory partial differential equations Point Boundary Value quadratic and non-quadratic quadratic error measure quadratic performance index rate of convergence scheme solved in backward space spacial Store U(x,t subject to boundary t-tf terminal condition thesis tion truncation error uQu'dxdx v/s number variation vibration wave equation weight factors