## Applied Mathematical Modelling |

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algorithm analysis analytical applied approximation assumed behaviour boundary conditions boundary element boundary element methods Brebbia calculated coefficient components computed concentration considered constant corresponding costs curve defined density derivatives determined developed differential equations diffusion discretization displacement distribution dynamic effect elastic element method energy Engineering error estimated evaluated example finite difference finite element finite element method flow forecast formulation Galerkin given grid income increase initial input integral Legendre polynomials linear load load duration curve Math mathematical modelling matrix matrix scheme mesh nodes nonlinear obtained operating optimal optimal control ordinary differential equations paper parameters partial differential equations pedestrian plume pollution polynomials population present problem procedure production region Research scheme shown in Figure simulation solution solved Southampton Statistical step stochastic stress structure Table techniques theory tion University University of Southampton upstream values variables variation vector velocity zero