Approximate solution of ordinary linear differential equations with analytical complex functions coefficient by means of Taylor matrix method

Abstract

Let f, p, q, r be analytical functions in D with complex variables and complex values, where D⊆ C is a simple connected domain of the complex plane in this study. We give approximative solutions of nonhomogenous ordinary differential equation p(z)y ⁽²⁾ (z)+q(z)y ⁽¹⁾ (z)+r(z)y(z)=f(z) via Taylor matrix method. Then we illustrate these solutions by some given applications.

Keywords:

• Ordinary linear differential equation
• Analytical complex function
• Taylor matrix method
• Approximative solution

Acknowledgements

We wish to express our gratitude to Mehmet Sezer for his invaluable guidance.