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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, Punjab University Journal of Mathematics, Volume 48, Issue 2.
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