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To find the minima of an energy functional, is a well known
problem in physics and engineering. Sobolev gradients have proven to
be affective to find the critical points of a functional. Here, we introduce
a similar approach to find the solution of nonlinear Klein Gordon equation (NKGE) in a finite-element setting. The results are compared using
Euclidean, weighted and unweighted Sobolev gradients. We also compare the results with Newton’s method for a test problem and show that
the presented method is better than Newton’s method in this case.
Nauman Raza. (2016) Application of Sobolev Gradient Method to Solve Klein Gordon Equation, , Volume 48, Issue 2.
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