Abstract: In this paper, collocation based cubic B-spline and
extended cubic uniform B-spline method are considered for
solving one-dimensional heat equation with a nonlocal initial
condition. Finite difference and θ-weighted scheme is used for
time and space discretization respectively. The stability of the
method is analyzed by the Von Neumann method. Accuracy of
the methods is illustrated with an example. The numerical results
are obtained and compared with the analytical solutions.