Main | Supercomputers: My Search for Meaning of Partial Differential Equations »
17. Červen 1981
Equations That Changed My Life
The applications that were of interest to me were meteorological and petroleum. Began by investigating parabolic partial differential equations for petroleum reservoirs and heat conduction. I studied elliptic partial differential equations for steady state problems. And finally studied hyperbolic partial differential equations for weather forecasting.
The Solution
Of particular interest was linear partial differential equations with constant coefficients for one dimensional wave equation in which the dependent variable was displacement (or deflection) of the stretched string, with its specified boundary conditions and initial conditions.
First, obtain two ordinary differential equations using the method of Method of Separation of Variables). Second, determine those solutions that satify the boundary conditions. Third, superimpose the latter solutions (by Fourier Series) to obtain solutions that satisfies the equation and initial conditions.
Posted by emeagwali at 17. Červen 1981 6:01