Numerical Approximations to Volterra's Population Model 1.0

The nondimensional form of Volterra's model for population growth in a closed system is given byk*(du/dt) = u - u^2 - u int_0^t u(x) dxThis gui allows the user to input the initial population u0, nondimensional constant k, final time Tmax and the number of mesh points M. By clicking on the appropriate button, the user can produce plots using various numerical methods.The "toxicity term" is the integral int_0^t u(x) dx. The panels "Trapezium Rule on Toxicity term" and "Simpson's Rule on Toxicity term" first apply a quadrature rule to the toxicity term and then use the designated numerical method to solve the resulting system. For more information see (1).For a thorough analysis of the problem see:1. Kevin G. TeBeest, Numerical and analytical solutions of Volterra's population model, SIAM Rev. 39 (1997), no. 3, 484{493.2. R. D. Small, Population growth in a closed system, SIAM Review 25 (1983), no. 1, 93{95.

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Platforms:	PHP
Keyword:	Analytical,  Apply,  Designated,  Information,  Integral,  Method,  Panels,  Population,  Quadrature,  Quotsimpson,  Quottrapezium,  Resulting,  Review,  Small,  Solutions,  Solve,  Toxicity
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