Error and variance of solution to the stochastic heat conduction problem by multiquadric collocation method

Abstract

Error and variance of the solution to the heat conduction problem having stochastic initial and boundary conditions are determined by a formulation based on a meshless method known as the multiquadric collocation method. This formulation expresses the solution in terms of initial and boundary conditions. Inspection of solutions to two test problems reveals that a large value of the shape parameter, which is the free parameter of multiquadrics, should not be used for a stochastic problem because it may lead to a solution that is too sensitive to uncertainties in boundary and initial conditions.