Solving 4th order nonlinear Differential Equation using bvp4c

Sumit Yelpale

2021 4 12

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I am new to matlab and I want to solve above equation using matlab bvp4c.

The boundary conditions are -

I want to plot the following graph( only the bottom cure and not all the curves) -

But my code gives a different graph.

Can anyone please help me?

The matlav code i am trying is as follows-

function dxdy = mat4ode(~,y)
E=169e9; % YMod
w=10e-6; % Width of beam
t=2e-6; % Thickness of beam
I=(w*(t^3))/12; % Moment of intertia
V=2.3; % Voltage
e0=8.854187817e-12; % VPerm
e1 = 7.5*e0;
d1 = 20e-9;
h0=2e-6;
qx = (V^2*w/(2*E*I))*(1 + 0.65*(h0+y(1))/w)/(e0*( d1/e1 + (h0+y(1))/e0 )^2);
dxdy=[y(2)
      y(3)
      y(4)
      qx]; %4th order equation
end
function res = mat4bc(ya,yb)
res=[ya(1) % u=0 at x=0
  ya(2) % du/dx=0 at x=0
  yb(3) % d2a/dx2=0 at x=L
  yb(4)]; % d3a/dx3=0 at x=L
end
function mat4bvp
options = bvpset('RelTol', 1e-8, 'AbsTol', 1e-8);
i =0;
solinit = bvpinit(linspace(0,450e-6,100),[i i i i]);  % Range of x and the Initial guess
sol = bvp4c(@mat4ode,@mat4bc,solinit,options);
x = linspace(0,450e-6);
y = deval(sol,x);
h = 2e-6 - y(1,:);
plot(1e6*sol.x,1e6*h);
xlim([0,450])
ylim([0,2])
end

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Sumit Yelpale 2021-4-26

I tried to solve the equation again by modifying the code and i got the graph whih is colse to the top curve in the above graph. Can anyone help me please.

Thank you

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