Coefficient estimation in a first-order nonlinear hyperbolic Cauchy problem |
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Authors: | K A Grasse L W White |
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Institution: | (1) Department of Mathematics, University of Oklahoma, Norman, Oklahoma |
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Abstract: | This paper deals with the estimation and approximation of coefficient function in a first-order, nonlinear, hyperbolic Cauchy problem. The estimation is accomplished by minimizing a functional which measures the error between a finite set of given observations and the corresponding values of the solution generated by the coefficient function. A class of admissible coefficient functions is defined, and it is proved that minimizing coefficient function always exists within this class. We also develop an approximation by a sequence of solutions of associated finite-dimensional minimization problems. |
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Keywords: | Coefficient estimation spline approximation Euler method Cauchy problems |
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