Efficient quadrature rules for a class of cordial Volterra integral equations: A comparative study

‎A natural algorithm with an optimal order of convergence is proposed for numerical solution of a class of cordial weakly singular Volterra integral equations‎. ‎The equations of this class appear in heat conduction problems with mixed boundary conditions‎. ‎The algorithm is based on a representation of the solution and compound Gaussian quadrature rules with graded meshes‎. ‎A comparative study is carried out‎, ‎which points out that the proposed method is the most efficient one among other existing methods‎. ‎In fact‎, ‎the results of this paper introduce a most-efficient decisive-choice for computing the solution of the heat conduction model‎.