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A platform for research: civil engineering, architecture and urbanism
Physical control of numerical solution of parabolic equations
Abstract A simple, efficient, powerful numerical method for solving linear, one-dimensional parabolic differential equations is described. The method consists in placing external disturbances whose intensities are found by recurrence so as to meet specified boundary conditions by collocation. The equation can have variable coefficients and the boundaries can move as continuous functions of time. Boundary conditions must be piecewise continuous. The method does not always converge and when it does it may converge to a wrong answer. Sufficient conditions are given for convergence; they are also necessary for certain large classes of problems. Necessary and sufficient conditions are also given for convergence to be to the correct answer. When these are not met it is possible to adjust the answer to which the method converges so that this answer coincides with the exact values. One way is to monitor physical quantities. In so doing one can simultaneously correct for the effects of having erroneously estimated the parameters that characterise the medium. The method and manner of adjustment are illustrated by means of examples in soil consolidation. It is found that use of least squares is inadequate as a criterion of goodness of fit in problems governed by parabolic differential equations.
Physical control of numerical solution of parabolic equations
Abstract A simple, efficient, powerful numerical method for solving linear, one-dimensional parabolic differential equations is described. The method consists in placing external disturbances whose intensities are found by recurrence so as to meet specified boundary conditions by collocation. The equation can have variable coefficients and the boundaries can move as continuous functions of time. Boundary conditions must be piecewise continuous. The method does not always converge and when it does it may converge to a wrong answer. Sufficient conditions are given for convergence; they are also necessary for certain large classes of problems. Necessary and sufficient conditions are also given for convergence to be to the correct answer. When these are not met it is possible to adjust the answer to which the method converges so that this answer coincides with the exact values. One way is to monitor physical quantities. In so doing one can simultaneously correct for the effects of having erroneously estimated the parameters that characterise the medium. The method and manner of adjustment are illustrated by means of examples in soil consolidation. It is found that use of least squares is inadequate as a criterion of goodness of fit in problems governed by parabolic differential equations.
Physical control of numerical solution of parabolic equations
Rosenblueth, Emilio (author)
Engineering Analysis ; 2 ; 107-110
1985-01-01
4 pages
Article (Journal)
Electronic Resource
English
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