Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A method for solving spectral problems for the Sturm-Liouville equation ( p v ' ) ' - q v + λ r v = 0 based on the approximation of the Delsarte transmutation operators combined with the Liouville transformation is presented. The problem of numerical approximation of solutions and of eigendata is reduced to approximation of a pair of functions depending on the coefficients p, q and r by a finite linear combination of certain specially constructed functions related to generalized wave polynomials introduced by Khmelnytskaya et?al. (2013) and Kravchenko and Torba (2015). The method allows one to compute both lor and higher eigendata with an extreme accuracy. Several necessary results concerning the action of the Liouville transformation on formal pors arising in the method of spectral parameter por series are obtained as ll as the transmutation operator for the Sturm-Liouville operator 1 r ( d d x p d d x - q ) .
['Vladislav V. Kravchenko', 'Samy Morelos', 'Sergii M. Torba']
I am writing a research paper on a idea Liouville transformation, analytic approximation of transmutation operators and solution of spectral problems
[{"from": "human", "value": "I am writing a research paper on a idea Liouville transformation, analytic approximation of transmutation operators and solution of spectral problems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A method for solving spectral problems for the Sturm-Liouville equation ( p v ' ) ' - q v + \u03bb r v = 0 based on the approximation of the Delsarte transmutation operators combined with the Liouville transformation is presented. The problem of numerical approximation of solutions and of eigendata is reduced to approximation of a pair of functions depending on the coefficients p, q and r by a finite linear combination of certain specially constructed functions related to generalized wave polynomials introduced by Khmelnytskaya et?al. (2013) and Kravchenko and Torba (2015). The method allows one to compute both lor and higher eigendata with an extreme accuracy. Several necessary results concerning the action of the Liouville transformation on formal pors arising in the method of spectral parameter por series are obtained as ll as the transmutation operator for the Sturm-Liouville operator 1 r ( d d x p d d x - q ) ."}]