Optimizing parameters in ODE
조회 수: 1 (최근 30일)
이전 댓글 표시
Hi I have a set of experimental data. I want to fit this experimental data to first order differential equation of the form dy/dt = -a*n-b*n^2-c*n^3 to optimize the value of constants a,b and c. Can anyone help in this regards? I am new to matlab as this question might be too simple for others. Thanks in advance.
댓글 수: 0
채택된 답변
Star Strider
2019년 9월 18일
This is a simple, separable differential equation that you can likely solve by hand.
Using the Symbolic Math Toolbox:
syms a b c n y(t) y0
DEqn = diff(y) == -a*n-b*n^2-c*n^3;
Eqn = dsolve(DEqn, y(0)==y0)
fcn = matlabFunction(Eqn, 'Vars',{[a,b,c],t,n,y0})
produces:
Eqn =
y0 - t*(c*n^3 + b*n^2 + a*n)
fcn =
function_handle with value:
@(in1,t,n,y0) y0-t.*(in1(:,1).*n+in1(:,2).*n.^2+in1(:,3).*n.^3)
or more conveniently:
fcn = @(in1,t,n,y0) y0-t.*(in1(:,1).*n+in1(:,2).*n.^2+in1(:,3).*n.^3);
with ‘in1’ corresponding to [a,b,c] in that order. Supply values for ‘n’ and ‘y0’, then present it to the nonlinear parameter estimation function of your choice as:
objfcn = @(in1,t) fcn(in1,t,n,y0)
Or, since it is ‘linear in the parameters’ you can re-write it as a design matrix and use linear methods such as mldivide,\ to solve it as well.
댓글 수: 4
Star Strider
2019년 9월 24일
As always, my pleasure!
My code estimates the initial condition as well, estimating it as ‘b(4)’, in the printed results as ‘ic’. So an initial estimate for it shoulld be ‘B0(4)’.
추가 답변 (0개)
참고 항목
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!