Is it possible to get the value of 'A' in a table format of 11x4 dimension

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MINATI 2019-4-18

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/457265-is-it-possible-to-get-the-value-of-a-in-a-table-format-of-11x4-dimension

评论： Walter Roberson 2019-5-1

function main
format long
Pr=0.72;
xa=0;xb=2;
solinit=bvpinit(linspace(xa,xb,11),[0 0 0 1 0]);
sol=bvp4c(@ode,@bc,solinit);
x=linspace(xa,xb,11);
sxint=deval(sol,x);
f0 = deval(sol,0);
P=f0(3);,Q=f0(5);
f=x.^2*(P/2)+x.^5*(P^2)/120-x.^3*(1/6)-x.^4*(Q/24)-x.^8*(P^3)*(13/40320)+x.^7*(P*Q)/1008+x.^7*(Pr*P*Q)/1680+...
    x.^11*(P^4)*(229/13305600)-x.^10*(P^2)*Q*Pr^2*(1/40320)-x.^10*(P^2)*Q*Pr*(37/1209600)+...
    x.^9*(P^2)/20160-x.^10*(P^2)*Q/22400-x.^9*(Pr*Q^2)/120960-x.^8*Q*Pr/13440+x.^8*Q/8064+x.^9*Q^2/72576;
g=1+x.*Q-x.^4*Pr*P*Q/8+x.^7*P^2*Q/56-x.^10*P^3*Q*Pr*(13/1209600)-x.^9*P*Pr^2*Q^2*(19/13440)-...
    x.^8*P*Q*Pr^2/128- x.^9*P*Pr*Q^2/24192;
function res=bc(ya,yb)
res=[ya(1); ya(2); yb(2); ya(4)-1;  yb(4)];  
end
 function dydx=ode(x,y)    
 dydx=[y(2);  y(3);  -3*y(1)*y(3)+2*y(2)^2-y(4);  y(5);  -3*Pr*y(1)*y(5)];              
 end
A = [x; sxint(4,:);g;E2]';
end
%%%   Is it possible to get the value of 'A' in a table format of 11x4 dimension

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Walter Roberson 2019-4-30

在 MATLAB Online 中打开

The equation is

(229*P^4)/13305600*x^11 + (-1/40320*P^2*Q*Pr^2 - 37/1209600*P^2*Q*Pr - 1/22400*P^2*Q)*x^10 + (1/20160*P^2 - 1/120960*Pr*Q^2 + 1/72576*Q^2)*x^9 + (-13/40320*P^3 - 1/13440*Q*Pr + 1/8064*Q)*x^8 + (1/1008*P*Q + 1/1680*Pr*P*Q)*x^7 + P^2/120*x^5 - Q/24*x^4 - 1/6*x^3 + P/2*x^2

The first derivative of this will have an x^1 term and a 0 x^0 (constant) term. Substitute in x = 0 and since that is 0 to various powers multiplied by things, you get 0 for all of them and there is no constant term to add, so you will get 0 for f'(0)

The second derivative of this will have an x^0 (constant) term of P. Substitute in x = 0 and all the other terms would become 0 and you would get P for f''(0)

The function is not a non-vanishing one.

If you want to ask about other hypothetical functions, then (A) Do you have the symbolic toolbox; and (B) what are the known properties of the function, if you are not permitted to read the properties out of the defining expression (such as if you were given a function handle.) Is it real-valued? Is the derivative known to be real-valued at 0? What is the region in which we can assume that the function is continuous C1 (continuous in the first derivative) ?

MINATI 2019-4-30

oook

thanks Walter

Walter Roberson 2019-5-1

Coefficient may be approximate. You can estimate the degree by looking at the number of leading coefficients that are approximately 0. You can also estimate by starting with a high degree fit and extracting the coefficient mentioned and then reducing the degree and examining again. When the coefficient changes drastically then you have gone one step too far.

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