# Equations and Boundary conditions are Unequal

조회 수: 1 (최근 30일)
MINATI PATRA 2023년 8월 14일
댓글: Torsten 2023년 8월 15일
%%% THe present code is of the attached (Model#02) pdf, need modification to run.
%%% REFERENCE: This type of work was done in DOI: 10.1002/num.22672 (More in size, so cant be uploaded)
main()
Unrecognized function or variable 'S'.

Error in solution>main/ode (line 21)
figure(10),plot(x,S(2,:),'-b','LineWidth',1.5),hold on

Error in bvparguments (line 105)
testODE = ode(x1,y1,odeExtras{:});

Error in bvp5c (line 129)
bvparguments(solver_name,ode,bc,solinit,options);

Error in solution>main (line 6)
xa = 0; xb = 5; solinit = bvpinit(linspace(xa,xb,100),[0 1 0 1 0 1 0 1 0 1 0 1]); sol = bvp5c(@ode,@bc,solinit); x = linspace(xa,xb,100); S = deval(sol,x);
function main
We = 2; n = 0.5; M = 1; Pr = 7; Rd = 0.5; Tw = 1.5; Nt = 0.3; Nb = 0.5; Ec = 0.3; Q = 0.5; Le = 2; K = 0.1; D1 = 0.1;
m = 0.5; E = 0.1; Lb = 0.5; Pe = 2; D2 = 1; S1 = 0.2; S2 = 0.2; Om = 0.5;
xa = 0; xb = 5; solinit = bvpinit(linspace(xa,xb,100),[0 1 0 1 0 1 0 1 0 1 0 1]); sol = bvp5c(@ode,@bc,solinit); x = linspace(xa,xb,100); S = deval(sol,x);
function BC = bc(ya,yb)
BC = [ya([1,4]); ya(2) - S1; ya([6,8,10]) - 1; yb([6,8,10]); yb(2) - S2; yb(4) - Om];
end
function EQ = ode(x,y)
Af = (1+(We*y(3))^2)^((n-1)/2) + (n-1)*(We*y(3))^2*(1+(We*y(3))^2)^((n-3)/2); Ag = (1+(We*y(5))^2)^((n-1)/2) + (n-1)*(We*y(5))^2*(1+(We*y(5))^2)^((n-3)/2);
At = 4*Rd*(Tw-1)*y(7)^2*(1+(Tw-1)*y(6))^2; X = - E/(1+D1*y(6));
EQ = [ -2*y(2);
y(3); (M*y(2) + y(2)^2 - y(4)^2 + y(1)*y(3))/Af;
y(5); (M*y(4) + 2*y(2)*y(4) + y(1)*y(5))/Ag;
y(7); (Pr/At)*( y(1)*y(7) - Nt*y(7)^2 - Nb*y(7)*y(9) - Ec*(y(3)^2 + y(5)^2) - M*Ec*(y(2)^2 + y(4)^2) - Q*y(6) );
y(9); Pr*Le*( y(1)*y(9) + K*(1+D1*y(6))^m*y(8)*exp(X) - (Nt/Nb)*((Pr/At)*( y(1)*y(7) - Nt*y(7)^2 - Nb*y(7)*y(9) - Ec*(y(3)^2 + y(5)^2) - M*Ec*(y(2)^2 + y(4)^2) - Q*y(6) )) );
y(11); Lb*y(1)*y(11)+ Pe*( y(9)*y(11) + (D2 + y(10)) )*Pr*Le*( y(1)*y(9) + K*(1+D1*(y(6))^m)*y(8)*exp(X) - (Nt/Nb)*((Pr/At)*( y(1)*y(7) - Nt*y(7)^2 - Nb*y(7)*y(9) - Ec*(y(3)^2 + y(5)^2) - M*Ec*(y(2)^2 + y(4)^2) - Q*y(6) ) ))
];
figure(10),plot(x,S(2,:),'-b','LineWidth',1.5),hold on
end
figure(2),plot(x,S(2,:));hold on
end

댓글을 달려면 로그인하십시오.

### 채택된 답변

Walter Roberson 2023년 8월 14일
이동: Walter Roberson 2023년 8월 14일
S is the output of the deval() and so is not available until after the bvp5c has been run. But the ode function wants to plot S, which requires S be defined but it is not defined until after the ode is finished.
Your plotting should be moved to before the bc function definition.
Meanwhile, your ode function needs to return a column vector of length 12, same length as your initial condition; at the moment it is only length 11.
main()
ans = 1×2
11 1
Error using bvparguments
Error in calling BVP5C(ODEFUN,BCFUN,SOLINIT):
The derivative function ODEFUN should return a column vector of length 12.

Error in bvp5c (line 129)
bvparguments(solver_name,ode,bc,solinit,options);

Error in solution>main (line 7)
sol = bvp5c(@ode,@bc,solinit);
function main
We = 2; n = 0.5; M = 1; Pr = 7; Rd = 0.5; Tw = 1.5; Nt = 0.3; Nb = 0.5; Ec = 0.3; Q = 0.5; Le = 2; K = 0.1; D1 = 0.1;
m = 0.5; E = 0.1; Lb = 0.5; Pe = 2; D2 = 1; S1 = 0.2; S2 = 0.2; Om = 0.5;
xa = 0; xb = 5;
solinit = bvpinit(linspace(xa,xb,100),[0 1 0 1 0 1 0 1 0 1 0 1]);
sol = bvp5c(@ode,@bc,solinit);
x = linspace(xa,xb,100);
S = deval(sol,x);
figure(10),plot(x,S(2,:),'-b','LineWidth',1.5),hold on
function BC = bc(ya,yb)
BC = [ya([1,4]); ya(2) - S1; ya([6,8,10]) - 1; yb([6,8,10]); yb(2) - S2; yb(4) - Om];
end
function EQ = ode(x,y)
Af = (1+(We*y(3))^2)^((n-1)/2) + (n-1)*(We*y(3))^2*(1+(We*y(3))^2)^((n-3)/2); Ag = (1+(We*y(5))^2)^((n-1)/2) + (n-1)*(We*y(5))^2*(1+(We*y(5))^2)^((n-3)/2);
At = 4*Rd*(Tw-1)*y(7)^2*(1+(Tw-1)*y(6))^2; X = - E/(1+D1*y(6));
EQ = [ -2*y(2);
y(3); (M*y(2) + y(2)^2 - y(4)^2 + y(1)*y(3))/Af;
y(5); (M*y(4) + 2*y(2)*y(4) + y(1)*y(5))/Ag;
y(7); (Pr/At)*( y(1)*y(7) - Nt*y(7)^2 - Nb*y(7)*y(9) - Ec*(y(3)^2 + y(5)^2) - M*Ec*(y(2)^2 + y(4)^2) - Q*y(6) );
y(9); Pr*Le*( y(1)*y(9) + K*(1+D1*y(6))^m*y(8)*exp(X) - (Nt/Nb)*((Pr/At)*( y(1)*y(7) - Nt*y(7)^2 - Nb*y(7)*y(9) - Ec*(y(3)^2 + y(5)^2) - M*Ec*(y(2)^2 + y(4)^2) - Q*y(6) )) );
y(11); Lb*y(1)*y(11)+ Pe*( y(9)*y(11) + (D2 + y(10)) )*Pr*Le*( y(1)*y(9) + K*(1+D1*(y(6))^m)*y(8)*exp(X) - (Nt/Nb)*((Pr/At)*( y(1)*y(7) - Nt*y(7)^2 - Nb*y(7)*y(9) - Ec*(y(3)^2 + y(5)^2) - M*Ec*(y(2)^2 + y(4)^2) - Q*y(6) ) ))
];
size(EQ)
end
figure(2),plot(x,S(2,:));hold on
end
##### 댓글 수: 4이전 댓글 2개 표시이전 댓글 2개 숨기기
MINATI PATRA 2023년 8월 15일
I think if first equation is differentiated again to make it a second order ODE, problem can be solved.
Torsten 2023년 8월 15일
You generate an artificial degree of freedom by this differentiation. Depending on the second boundary condition you impose you may or may not reproduce the solution of the original problem (first-order ODE with only one boundary condition).
Test it for a simple example.

댓글을 달려면 로그인하십시오.

### 카테고리

Help CenterFile Exchange에서 Ordinary Differential Equations에 대해 자세히 알아보기

### Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by