Abstract
The nonsingular, nonlinear Volterra integral equation of the second kind for the surface temperature of a sphere object to a general boundary condition is solved numerically by a linear multistep procedure based on the composite formula. A linearly increasing step size along with an alternating combination of Simpson's rule together with the trapezoid rule is used to carry out the numerical integration. A two-phase integration sequence is devised to eliminate an excessive number of linear steps for convection and radiation parameters greater than one. A linear boundary condition for which an analytical solution exists is used to test the accuracy of the numerical method, whereas the Stefan-Boltzmann law is considered as a nonlinear example of some physical significance. A finite-difference numerical calculation is also performed to verify that the integral method is computationally less expansive than the finite-difference formulation.
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