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STUDY OF THE EQUATION (1)

INTRODUCTION

I-CRITERION OF NUMERICAL STABILITY

1-dt=2.10-² and dx=5.10-²:
2-dt=10-² and dx=5.10-²:
3-dt=2.10-² and dx=2.10-²:
4-Conclusion:
II-EQUILIBRIUMS
1- Equilibriums and stability of (2)
2-Graph of equation (2) in the plane (u,P)
III-TRAJECTORIES
1-Curves of the equation (1) in the plane (x,t,u):
2-Curve u(x) for the last value of t:
3-Curve (P(x),u(x)) for the last value of t:
4-Curve (Pe(x),ue(x)) of the corresponding equilibrium:
IV-MATLAB PROGRAMS
1-Program ploting V'(u):
2-Programs ploting the equilibriums ue(x) of our equation:
3-Program ploting the curves u(x,t) of our equation:
4-:Program ploting the profile u(x) for t the last value of time:
5-Program ploting the profile u(P) for t the last value of time:
CONCLUSION
 
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