Hi my friends
I am trying to solve system of nonlinear complex equations which obtained from vibration of beam with classical BC. these BC cause the complexity of the characteristics equation, so I looking for the fully numerical algorithm without need to direct function and it's derivatives (such as Newton method).
Thanks a lot.
Can you give some examples of the type of equations you have, but more particularly what you mean by non-classical boundary conditions?
Richard Epenoy
Hi again dear Dr. Epenoy
Yes I tried, but unfortunately it doesn't work (e.g. I tried to solve my equation in MAPLE but given roots were not true), the final equation is very long and complex, so I have to solve numerically
D. Andrew S. Rees
Hi dear Dr. Rees,
I have rotational spring and damper in both end
That doesn't help me! What are the equations? I cannot match the difficulty you are facing with anything in my own experience if I can't see the equations!
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.218.9039&rep=rep1&type=pdf
This paper proposes a new perspective for solving systems of complex nonlinear equations by simply viewing them as a multiobjective optimization problem. Every equation in the system represents an objective function whose goal is to minimize the difference between the right and left terms of the corresponding equation. An evolutionary computation technique is applied to solve the problem obtained by transforming the system into a multiobjective optimization problem. The results obtained are compared with a very new technique that is considered as efficient and is also compared with some of the standard techniques that are used for solving nonlinear equations systems. Several well-known and difficult applications (such as interval arithmetic benchmark, kinematic application, neuropsychology application, combustion application, and chemical equilibrium application) are considered for testing the performance of the new approach. Empirical results reveal that the proposed approach is able to deal with highdimensional equations systems.
Now, the objectivity and the functioning of the equations in question has much to do with its roots. Nonlinear complex equations has pseudo-roots in ODEs which can be resolved numerically and the new approach seems to be a bit earlier in reaching the roots as compared to the standard version of solving dynamical systems. Nonetheless, the dimensions of higher rooted equations are explicit in the nonlinear complex equations. The applicability in real life is the issue here?
if you need to obtain a single solution, you can try to calculate derivatives in some gradient method numerically or use some metaheuristics.
Please send me your system, and I will try solve it with detailed description.
Best regards,
Sharif E. Guseynov
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