LAUSR

Reduced basis methods (RBMs) in the collocation framework provide both high accuracy approximate solution and efficient error estimate to parametrized partial differential equations (PDEs). Reduced collocation method (RCM) has so far been applied for steady problems (Chen and Gottlieb in J Sci Comput 55(3):718–737, 2013). In this paper, we extend this methodology to time-dependent parametrized PDEs, so the novelty of this paper is the consideration of time in the presentation of formulas and solution of the problem. RBMs idea in collocation method is attractive for theirsimplicity of implementation and efficient result, especially for time-dependentproblems. For such case, we combine the proper orthogonal decomposition (POD)technique in time with greedy algorithm in parameter for producing optimal reduced basis (RB) space. Numerical results for time-dependent convection–diffusion problem and Burgers’ equation illustrate the highly accurate and efficiency of the presented method.