initial condition ODE45?

Can anyone tell me how to implement these initial condition in ODE45?

i have this differentiel equation to resolve:

thanks

Answer 1

[John D'Errico]

You cannot. That is to say, not directly. I suppose you could formulate it as a shooting method, in which case it becomes a nonlinear problem for fsolve.

But ODE45 is an initial value solver. You have conditions at THREE distinct locations. That makes this more of a boundary value problem.

I see some additional issues. What is S? Is S a known function?

Depending on what is S, I might suggest using some other general scheme to solve ODE problems, perhaps collocation.

[silos ab]

thank you for your answers, I will be very grateful if you can help me to correct the code below

this is my equation:

"S" is a function call "SS" in code

clc; clear all; close all;clf;
%% les données:
vs=0.25;     
p=0.5;       
Zp= 2000;    
h=18000;     
R=5100;      
Dp=500;     
E=210;      
A=196350;    
G=81;        
v=0.3;     
Es=96.14;    
Ks=2;       
I=3.06796E9; 

EI=E*I;
Gp=Es*h/6*(1+vs);                
Kp=(1-vs)*Es/((1+vs)*(1-2*vs)*h);   

%% calcul coefficient:
a =-(((Dp*Kp*EI)+(Dp*Gp*G*A*Ks))/(EI*(G*A*Ks+Gp*Dp)));    
b =(Dp*Kp*G*A*Ks)/(EI*(G*A*Ks+Gp*Dp));
c =Dp*Gp/(G*A*Ks+Gp*Dp);

%%  calcul de s(x)
syms x f(x) X Y 

i=0.175*Zp+0.325*(Zp-h);
smax=0.313*p*Dp^2/i;
ss= smax*exp(-0.5*x.^2/i^2);

%% dériver de s(x): f(x)= c*S""-a*s"+b*s
syms x f(x) X Y 
D2ss = diff(ss,x,2);
D4ss = diff(ss,x,4);
ssdiv=vpa(simplify(c*D4ss+a*D2ss+b*ss),3);
 
D2f = diff(f,x,2);
D4f = diff(f,x,4);
fdiv=D4f+a*D2f+b*f;

ode =fdiv==ssdiv;

[VF,Sbs] = odeToVectorField(ode);
odefcn = matlabFunction(VF, 'Vars',{x,Y});

[X,Y] = ode45(odefcn, [-15 15], [0 0 0 0]);
figure
plot(X,Y)
grid
legend(string(Sbs))