Rogia Ahmed Mahmmoud Abdallah2017-08-062017-08-062016http://hdl.handle.net/123456789/4653Abstract In this thesis we presented two mathematical models for herbivore/vegetation interactions. The first model is a metaphysiological model in a single patch environment. The second model is a metaphysiological model for herbivore and vegetation interactions in two patches environment. We applied the multistage spectral relaxation method (MSRM) to solve these models. The MSRM method was presented to solve initial-value problems when the time domain is decomposed to sub-domains. We compared our results to the results that obtained from the MATLAB built-in function ode45.الرياضياتMathematical Statistics