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This hybrid analytic-numerical method is more accurate and needs less computer time than full-numerical methods because it needs no grid generation, the derivatives of all parameters can be easily and exactly computed, and the NSL’s PDEs are satisfied exactly (at an arbitrary number of chosen points).

We have proposed an efficient iterative domain decomposition method that solves general convection-diffusion singular perturbation problems. Our specific application involves a piecewise constant diffusion coefficient. We have established sufficient conditions for the convergence of the method, identified suitable values of the relaxation parameter , and started investigations into the rate of convergence. The method was implemented to (2) to solve test problems.

Full details of the proofs of these assertions will appear in a future publication.

Requirements for the safety and nutritional adequacy of infant formula are set by legislation and aim for the best possible substitute for human milk with regard to growth, development and biological effects. This is, however, a continuous process and has to be supported by science-driven innovative activities of manufacturers and be confirmed by adequate clinical studies performed according to agreed standards.

Since Taylor series can be constructed for smooth functions, for the solution of an ordinary differential equation, and for an inverse function, we can approximate certain integrals in various ways by means of such series, in quite an effective manner.

We have proposed an efficient iterative domain decomposition method that solves general convection-diffusion singular perturbation problems. Our specific application involves a piecewise constant diffusion coefficient. We have established sufficient conditions for the convergence of the method, identified suitable values of the relaxation parameter , and started investigations into the rate of convergence. The method was implemented to (2) to solve test problems.

Full details of the proofs of these assertions will appear in a future publication.

Requirements for the safety and nutritional adequacy of infant formula are set by legislation and aim for the best possible substitute for human milk with regard to growth, development and biological effects. This is, however, a continuous process and has to be supported by science-driven innovative activities of manufacturers and be confirmed by adequate clinical studies performed according to agreed standards.

Since Taylor series can be constructed for smooth functions, for the solution of an ordinary differential equation, and for an inverse function, we can approximate certain integrals in various ways by means of such series, in quite an effective manner.

Over the years, the Burton and Miller method has been shown to be a theoretically reliable method for determining the acoustic field radiated or scattered by an object. However, in practice, nearly all of the earlier work on this problem was restricted to using a piecewise constant approximation and there has always been the problem of how to evaluate the integral operator which involves the second derivative of the Green’s function beyond the piecewise constants.

The work in the paper shows how this problem can be overcome; by using a singularity subtraction technique, one manages to avoid introducing any volume integrals. This new formulation allows a much wider class of basis functions to be considered. The numerical results show that the higher-order piecewise polynomials considered here give considerably more accurate results.

We have proposed an efficient iterative domain decomposition method that solves general convection-diffusion singular perturbation problems. Our specific application involves a piecewise constant diffusion coefficient. We have established sufficient conditions for the convergence of the method, identified suitable values of the relaxation parameter , and started investigations into the rate of convergence. The method was implemented to (2) to solve test problems.

Full details of the proofs of these assertions will appear in a future publication.

Since Taylor series can be constructed for smooth functions, for the solution of an ordinary differential equation, and for an inverse function, we can approximate certain integrals in various ways by means of such series, in quite an effective manner.