Numerical Solution for High-Order Linear Complex Differential Equations By Hermite Polynomials

Abstract

ÖZET: Bu makalede lineer kompleks diferansiyel denklemleri hermite polinomları vasıtasıyla nümerik çözümünü sağladık ve iki test problemine uyguladık. Tam çözümler ile nümerik çözümleri tablo ve grafikler ile karşılaştırdık. Sonuç olarak metodumuzun güvenilir, pratik ve kullanışlı olduğunu gördük.

Solution of n.th Order Constant Coefficients Complex Partial Derivative Equations by Using Fourier Transform Method

“…Similarly numerical solutions of linear complex differential equations have been studied with complex operational matrix method in [12]. In studies [13] and [14], the numerical solutions of linear complex differential equations have been obtained by using Legendre and Hermite polynomials. In this study, the equations of the following form has been studied.…”

Numerical solution for (2 + 1)‐dimensional time‐fractional coupled Burger equations using fractional natural decomposition method

“…The mathematical groundwork for derivatives of fractional order was laid through combined efforts of pioneers such are Liouville, Riemann, Caputo, Miller and Ross, Podlubny, and others. The theory of fractional‐order calculus has been related to practical projects, and it has been applied to chaos theory, signal processing, electrodynamics, fluid dynamics, finance, and other areas …”

“…The theory of fractional-order calculus has been related to practical projects, and it has been applied to chaos theory, 8 signal processing, 9 electrodynamics, 10 fluid dynamics, 11 finance, 12 and other areas. [13][14][15][16][17][18][19][20][21][22][23] The Burgers equations are the fundamental nonlinear partial differential equations that exist in distinct connected branches of science and technology. These equations can be seen as a simplified model of fluid dynamics, and it is used as a computational tool in order to deal with more complex problems.…”