#1




differential eq with square root
Hi!
I have to solve a system of two coupled nonlinear ordinary differential equations. In the function that defines the system there are terms with square root of the dependant variables. I tried to solve the system numerically but in the nmerical solution I get violent oscillations. Then I realized that the same problem appears in the numerical solution of this very simple exactly solvable differential equation: x'(t)=(1x(t))^(1/2) with initial condition x(2.1)=0.9975. The exact solution is x(t)=(1/4)(4tt^2). It seems to me that the problem is the square root (1x(t))^(1/2). When the numerical solution approach an extremum, then x'(t) and (1x(t))^(1/2) both approach zero. But then (1x(t)) also approaches zero, and in fact (1x(t)) takes negative values, that makes the square root imaginary. I explore the situation with the fourthorder RungeKutta method with step h=0.2 and in the firt iteration I find the complex value: x(2.1)=1.00463+ 0.0042963 I The same happens with the Euler method and the MidPoint Method Any hint of how to get the correct numerical solution of this equation??? Thanks a lot! 
Thread Tools  
Display Modes  

