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Approximate Solutions Of Nonlinear Partial Differential Equations Using B-Polynomial Bases, Muhammad I. Bhatti, Md. Habibur Rahman, N. Dimakis
Approximate Solutions Of Nonlinear Partial Differential Equations Using B-Polynomial Bases, Muhammad I. Bhatti, Md. Habibur Rahman, N. Dimakis
Physics and Astronomy Faculty Publications and Presentations
A multivariable technique has been incorporated for guesstimating solutions of Nonlinear Partial Differential Equations (NPDE) using bases set of B-Polynomials (B-polys). To approximate the anticipated solution of the NPD equation, a linear product of variable coefficients ai(t) and Bi(x) B-polys has been employed. Additionally, the variable quantities in the anticipated solution are determined using the Galerkin method for minimizing errors. Before the minimization process is to take place, the NPDE is converted into an operational matrix equation which, when inverted, yields values of the undefined coefficients in the expected solution. The nonlinear terms of the NPDE are combined in the …
26 Results Of Hyperbolic Partial Differential Equations In B-Poly Basis, Muhammad I. Bhatti, Emilio Hinojosa
26 Results Of Hyperbolic Partial Differential Equations In B-Poly Basis, Muhammad I. Bhatti, Emilio Hinojosa
Physics and Astronomy Faculty Publications and Presentations
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 …