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During the past 50 yr there have been many methods developed for solving differential equations, both for closed form solutions and approximate methods. Improvements in digital computing capabilities have resulted in the refinement of finite difference methods. Recently the finite element method has been demonstrated to have wide application in solving engineering problems. Both finite difference and finite element methods have been utilized to solve problems where mathematical treatment was impractical or impossible. Utilizing finite difference or finite element techniques to solve differential equations can have several disadvantages. (1) The solution to a particular problem is represented as tabulated values at a finite number of grid points thus, the solution of one problem is difficult to utilize as input to another problem if required. (2) In many cases the selection of proper time increments and element size to obtain convergence is not straightforward and can involve considerable trial and error. (3) Computer core requirements can become very large in refining the solutions to an appropriate magnification. The Galerkin Method for solving differential equations, developed over 70 yr ago (Kantorovich and Krylov 1964), utilized extensively before the development of high speed computers, is becoming more popular again in the solution of complex problems. This method in many cases has advantages over finite element and finite difference methods, especially in problems dealing with simultaneous heat and mass transfer. It should be noted, however, that Galerkin
galerkin's method in agricultural engineering
Carson, W.M., Watts, K.C. and S.N. Sarwal 1979. GALERKIN's METHOD IN AGRICULTURAL ENGINEERING. Canadian Agricultural Engineering 21(2):125-130.
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