Numerical Solutions for Linear Integro–Differential Equations of Parabolic Type with Weakly Singular Kernels

In this paper we study numerical solutions by finite element for the following weakly singular parabolic integro-differential equation: (1.1) u t + A ( t ) u ( t ) + ∫ 0 t ( t − s ) − α B ( t , s ) u ( s ) d s = f ( t ) ,         in     Ω × J , u = 0 ,                     on     ∂ Ω × J , u ( ⋅   ,   0 ) = v ,                     on     Ω https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072140/faeac70b-e389-4ea4-8b5b-5a836c2a1f73/content/eq3923.tif"/>