{'fraction_non_alphanumeric': 0.028730305838739572, 'fraction_numerical': 0.0009267840593141798, 'mean_word_length': 5.033519553072626, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
An efficient algorithm for the solution of second order PDE’s using Taylor expansion polynomials

Abstract Taylor expansion method for the solution of second order PDE’s, is based on taking truncated Taylor polynomial about any point of the coefficients functions has been investigated by Kesan [3]. In this paper, we develop an algorithm for the solution of the PDE’s of the form f (x, y) uxx – g (x, y) uyy = h (x, y), with any boundary conditions, based on taking truncated Taylor polynomials about any point of the coefficients functions to obtain the augmented systems. We present a modified sparse technique to solve the obtained systems. We verify our proposed algorithms via numerical experiments, then we compare it with Kesan’s work and the finite difference method. The numerical results indicate that our algorithm is easily applicable on a wide range of PDE’s and give more accurate solutions than Kesan’s and the finite difference method. Also, it provides a reduction of both computational time and storage requirements without sacrificing the numerical stability.