My equation is dx1dA(t, a1, a2, A) =
-((u – A*diff(x1(t, a1, a2, A), t))*(A*diff(x1(t, a1, a2, A), A, t) + diff(x1(t, a1, a2, A), t)))/(a1^2*g)
how can i solve it in matlab?
MATLAB: How can i solve Partial differential equation
pde
Related Solutions
>> A = sym('a',[3 3]);>> b = sym('b',[3 1]);>> x = A\bx = (a1_2*a2_3*b3 - a1_3*a2_2*b3 - a1_2*a3_3*b2 + a1_3*a3_2*b2 + a2_2*a3_3*b1 - a2_3*a3_2*b1)/(a1_1*a2_2*a3_3 - a1_1*a2_3*a3_2 - a1_2*a2_1*a3_3 + a1_2*a2_3*a3_1 + a1_3*a2_1*a3_2 - a1_3*a2_2*a3_1) -(a1_1*a2_3*b3 - a1_3*a2_1*b3 - a1_1*a3_3*b2 + a1_3*a3_1*b2 + a2_1*a3_3*b1 - a2_3*a3_1*b1)/(a1_1*a2_2*a3_3 - a1_1*a2_3*a3_2 - a1_2*a2_1*a3_3 + a1_2*a2_3*a3_1 + a1_3*a2_1*a3_2 - a1_3*a2_2*a3_1) (a1_1*a2_2*b3 - a1_2*a2_1*b3 - a1_1*a3_2*b2 + a1_2*a3_1*b2 + a2_1*a3_2*b1 - a2_2*a3_1*b1)/(a1_1*a2_2*a3_3 - a1_1*a2_3*a3_2 - a1_2*a2_1*a3_3 + a1_2*a2_3*a3_1 + a1_3*a2_1*a3_2 - a1_3*a2_2*a3_1)Now, I'm not sure which substitutions would really help here; the ones you used in the 2*2 case you can get this way:
>> Z = sym('Z',[3 1]);>> xx = sym('x',[3 1]);>> simplify(subs(x(1)/b(1), b, Z.*xx))ans =(Z3*a1_2*a2_3*x3 - Z3*a1_3*a2_2*x3 - Z2*a1_2*a3_3*x2 + Z2*a1_3*a3_2*x2 + Z1*a2_2*a3_3*x1 - Z1*a2_3*a3_2*x1)/(Z1*x1*(a1_1*a2_2*a3_3 - a1_1*a2_3*a3_2 - a1_2*a2_1*a3_3 + a1_2*a2_3*a3_1 + a1_3*a2_1*a3_2 - a1_3*a2_2*a3_1))Dinesh,
Are you trying to simulate the evolution of a differential equation? Are you trying to solve the equation?
The differential equation:
is ordinary, not partial.
If you want to solve this equation and plot v(t) over time to compare the solution to the experimental values, you can use the dsolve function of Symbolic Math Toolbox.
The documentation page for dsolve contains examples to show you how to solve an ordinary differential equation. In addition, you can also take a look at this example page:
For example, you could solve the ODE above as follows:
>> syms k x(t)>> S = dsolve(diff(x) == k*(2-2.37*x)/2.12)S = (C3*exp(-(237*k*t)/212))/237 + 200/237Then, if you want to evaluate it, use matlabFunction to convert the expression to a function of C3, k and t:
>> v = matlabFunction(S)v = @(C3,k,t)C3.*exp(k.*t.*(-2.37e2./2.12e2)).*(1.0./2.37e2)+2.0e2./2.37e2You can now evaluate it. For example, for C3 and k equal to 1:
>> t = 0:0.01:10;>> y = v(1,1,t);Now display the plot:
>> plot(t,y)
Best Answer