Shimizu A., Aoki K. Application of invariant embedding to reactor physics

Academic Press, New York, 1972. – 184 pp.
Recently, the systematic use of invariance concepts and functional equations in mathematical physics has been named invariant embedding" by Richard Bellman. The invariant embedding approach is advantageous for computations by digital computer, since it reduces two-point boundary-value problems to initial value problems. The present monograph describes the application of the method of invariant embedding to radiation shielding and to criticality calculations of atomic reactors. The authors intend to show how this method has been applied to realistic problems, together with the results of applications which will be useful to shielding design.Formulation of the problem based on the invariant embedding principle.
Solutions of equations for simplified models.
Method of numerical solutions.
Reflection and transmission of gamma rays.Introduction to criticality calculations.
One-dimensional problem.
Two-dimensional problem.
Appendix.