Abstract
So far, there are no any publications for solving and obtaining a numerical solution of Volterra integro-differential equations in the complex plane by using the finite element method. In this work, we use the linear B-spline finite element method (LBS-FEM) and cubic B-spline finite element method (CBS-FEM) for solving this equation in the complex plane. We also discuss the error and convergence of the method. Furthermore, we give some numerical examples to substantiate efficiency of the proposed method.
Highlights
1 Introduction One of the first works in imaginary numbers was by the Persian mathematician AlKhwarizmi
Pa√ul Nahin gave a detailed description of imaginary numbers [1]
Gauss demonstrated that every polynomial equation of degree n with nonzero complex coefficients has n roots in complex numbers
Summary
One of the first works in imaginary numbers was by the Persian mathematician AlKhwarizmi. The first person who used them is Girolamo Cardano (1501–1576). Pa√ul Nahin gave a detailed description of imaginary numbers [1]. The symbol i instead of –1 was proposed by Euler (1707–1783). The interpretation of complex numbers as points in the plane was suggested by Carl Friedrich Gauss (1777–1855). Gauss demonstrated that every polynomial equation of degree n with nonzero complex coefficients has n roots in complex numbers. The complex functions and their integrals were studied by Gauss and Simon Denis Poisson (1781–1840). August Louis Cauchy (1789– 1857) published a large number of researches on the integral theorem and related concepts. George Bernhard Riemann (1826–1860) introduced the derivatives of functions of complex variables [2]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
