Numerical solution of calcium-mediated dendritic branch model

The standard algorithms for spatial discretizations of calcium-mediated dendritic branch models via finite difference methods are quite accurate, but they are also extremely slow. To improve computational efficiency we apply spatial discretization using a spectral collocation method. Simulations using the spectral collocation method are compared to the finite difference approach using a model for calcium-mediated restructuring with spine pruning. We find that the spectral collocation method is about fifteen times more efficient to achieve similar accuracy than the finite difference approach even though spectral collocation requires more steps.