Abstract
<p>A class of Schwarz problems with the conditions concerning the real and imaginary parts of high-order partial differentiations for polyanalytic functions was discussed first on the bicylinder. Then, with the particular solution to the Schwarz problem for polyanalytic functions, a Dirichlet problem for bi-polyanalytic functions was investigated on the bicylinder. From the perspective of series, the specific representation of the solution was obtained. In this article, a novel and effective method for solving boundary value problems, with the help of series expansion, was provided. This method can also be used to solve other types of boundary value problems or complex partial differential equation problems of other functions in high-dimensional complex spaces.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference25 articles.
1. X.-Z. Zhang, A. Khalid, M. Inc, A. Rehan, K. S. Nisar, M. S. Osman, Cubic spline solutions of the ninth order linear and non-linear boundary value problems, Alex. Eng. J., 61 (2022), 11635–11649. https://doi.org/10.1016/j.aej.2022.05.003
2. F. A. Shah, M. Irfan, K. S. Nisar, R. T. Matoog, E. E. Mahmoud, Fibonacci wavelet method for solving time-fractional telegraph equations with Dirichlet boundary conditions, Results Phys., 24 (2021), 104123. https://doi.org/10.1016/j.rinp.2021.104123
3. K. S. Nisar, J. Ali, M. K. Mahmood, D. Ahmad, S. Ali, Hybrid evolutionary pad$\acute{e}$ approximation approach for numerical treatment of nonlinear partial differential equations, Alex. Eng. J., 60 (2021), 4411–4421. https://doi.org/10.1016/j.aej.2021.03.030
4. J. Sander, Viscous fluids elasticity and function theory, Trans. Amer. Math. Soc., 98 (1961), 85–147.
5. W. Lin, T.-C. Woo, On the bi-analytic functions of type $(\lambda, k)$, Acta Scientiarum Naturalium Universitatis Sunyantseni, 1 (1965), 1–19.