Abstract—In this study, we examine the approximate solutions of complex differential equations in rectangular domains by using Euler polynomials. We construct the matrix forms of Euler polynomials and their derivatives to transform the considered differential equation to matrix equation with unknown Euler coefficients. This matrix equation is also equivalent to a system of linear algebraic equations. Linear system is solved by substituting collocation points into those matrix forms to get the unknown Euler coefficients. Determining these coefficients provides the approximate solutions of the given complex differential equations under the given conditions.

Index Terms—Euler polynomials, complex differential equations, collocation method.

The authors are with Celal Bayar University, Faculty of Arts & Science, Department of Mathematics, Muradiye Campus, 45030, Manisa, Turkey (email: necdet.bildik@cbu.edu.tr).

Cite: Necdet Bildik, Mehtap Tosun, Sinan Deniz, "Euler Matrix Method for Solving Complex Differential Equations with Variable Coefficients in Rectangular Domains," International Journal of Applied Physics and Mathematics vol. 7, no. 1, pp. 69-78, 2017.