Determination of an Unknown Heat Source from Integral Overdetermination Condition

Analytical and Numerical Investigation of two-dimensional Heat Transfer with Periodic Boundary Conditions

“…In the present paper, we prove the existence, uniqueness, and continuous dependence of the solution on the data and obtain the numerical solution by Fourier Method and Picard's successive approximation of the two-dimensional heat diffusion problem with periodic boundary conditions [14,27,28]. For numerical solution, implicit finite difference approximation is used.…”

“…In this study, three different schemes were used, namely, backward time centered space (BTCS) implicit scheme, the implicit Crandll's method, forward time centered space (FTCS) explicit scheme and the Dufort-Frankel threelevel techniques. Crank-Nicolson implicit scheme is used to solve numerically for one-dimensional heat diffusion equation with inverse coefficient by Baglan et al [27]. Kanca and Baglan solve the twodimensional heat diffusion equation with periodic boundary conditions analytically and numerically [28].…”

Solution of parabolic problem with inverse coefficient s(t) with periodic and integral conditions

“…The inverse problems are an area of great interest to many researchers [1,3,5,4]. Especially, periodic conditions are very used conditions especially in physics and engineering [2,1,3,6…”

Numerical Analysis of Volterra Integro-differential Equations with Caputo Fractional Derivative

“…The VIE was deduced from a nonlinear fractional differential equation in Assari and Dehghan (2019), where the authors used a meshless local Galerkin method to solve the model numerically. The readers may also consider the articles (Baglan et al 2018;Kanca and Mishra 2019;Mishra et al 2013a, b) and references therein to study about integral boundary conditions and integral type operators. Now it is quite obvious that one integral equation may contain a term with integer order derivative, then it is said to be the integro-differential equation(IDE).…”