Application of Numerical Methods in Design of Industrial Structures

Abstract

There are practices on application and optimisation problems. We deal with some mathematical results, comparisons, optimisations and conclusions upon different structures. The results show that each method has its strengths and weaknesses depending on the nature of the equation and the initial guess. The bisection method is the most robust and guarantees convergence, but it is also the slowest. Newton's method is the fastest and converges quadratically near the root, but it may fail for certain types of equations. The secant method is a compromise between speed and robustness, but it may suffer from slow convergence or oscillations. This article also discusses the sources of errors and limitations of the methods, as well as the applications of these methods in real-world problems. Moreover, we will deal with their application in engineering field mostly in civil engineering field as they have a wide application there and are also very useful methods. For instance we will use numerical methods to design hydraulic structures. Numerical methods are techniques by which the mathematical problems involved with the engineering analysis cannot readily or possibly be solved by analytical methods. the simplex algorithm are used to find optimal solutions to these problems. These methods involve iterative procedures that converge to the optimal solution.Approximation methods are used to simplify complex functions or data sets.