Spherical Spline Solution of the Heat Equation
AbstractWe consider a spline approximation to the solution of the heat equation on the unit sphere. The time derivative is approximatedby a backward divided difference resulting in an implicit method of order two. The differential equation on the sphere is solvedby means of spherical splines. Numerical experiments exhibit quadratic convergence for the time variable and at least quadraticconvergence with respect to the spacial variables. Spherical harmonics approximation is considered for the purpose of comparisonwith splines.