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The numerical solutions of ordinary and partial diÆerential equations (ODEs and PDEs) among others are of special importance for quantum mechanics problems. The wavefunctions of elementary particles in nuclei and the binding energies are calculated by the Schrödinger and Dirac equations. The last two decades or so, a large number of numerical algorithms have been employed to solve the eigen value problem. Such numerical methods the Artificial Neural Networks (ANN), genetic algorithms, direct diagonalization, and the finite elements method (FEM) among others. ANN and FEM were presented as the most reliable algorithms (e.g. MERLIN) to solve non-homogeneous ODEs and PDEs [1,3,2].

Nuclear muon capture rates by using relativistic muon wavefunctions