A two-variable process to estimate results of Hyperbolic Partial Differentiation (HPD) equations in a B-Polynomial (B-Poly) bases is established. In the proposed process, a linear product of variable coefficients and B-Polys is manipulated to express the predicted solution of the HPD equation. The variable coefficients of the linear mixture in the results are concluded using Galerkin technique. The HPD equation is converted into a matrix which when inverted provided the unknown coefficients in the linear mixture of the solution. The anticipated solution is constructed from the variable coefficients and B-Poly basis set as a product with initial conditions implemented. Both the effectiveness and precision of the process depend on the number of B-Polys employed in the results and degree of the B-polys utilized in the linear sequence. The current process is applied to solve four linear examples of the HPD equations with various initial conditions. An excellent agreement was found between exact and estimated results and in some cases estimates were exact. The current process renders a higher degree of efficiency and accuracy for solving the HPD equations. The process can be easily employed in other fields such as physics and engineering to solve complex PDEs in two variables.
Bhatti, Muhammad I., and Emilio Hinojosa. “26 Results of Hyperbolic Partial Differential Equations in B-Poly Basis.” Journal of Physics Communications, vol. 4, no. 9, IOP Publishing, Sept. 2020, p. 095010, doi:10.1088/2399-6528/abb24b.
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Journal of Physics Communications