AN O(H6) COLLOCATION METHODS FOR SECOND AND FOURTH ORDER ELLIPTIC EQUATIONS
Abstract
IN THIS THESIS WE DEVELOP AND ANALYZE OPTIMAL COLLOCATION METHODS FOR SECOND AND FOURTH ORDER TWO-POINT BOUNDARY VALUE PROBLEMS (LINEAR AND NON LINEAR). THESEDIFFERENTIAL EQUATIONS ARE CONSIDERED TO BE DEFINED IN SPACES R AND R2 AND THEIR SOLUTION SATISFIES SOME BOUNDARY CONDITIONS. THE APPROXIMATION SOLUTIONS AREPIECEWISE POLYNOMIALS OF DEGREE 5, IN THE SPACE C4. WE MAKE A THEORETICAL STUDYING OF THESE METHODS AND WE PROVE THEIR OPTIMAL CONVERGENCE. WE ALSO PRESENT THE COMPUTATIONAL BEHAVIOUR OF THE OPTIMAL QUINTIC SPLINE COLLOCATION METHOD.
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