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Mathematics plays an important role in many scientific and engineering disciplines. This book deals with the numerical solution of differential equations, a very important branch of mathematics. Our aim is to give a practical and theoretical account of how to solve a large variety of differential equations, comprising ordinary differential equations, initial value problems and boundary value problems, differential algebraic equations, partial differential equations and delay differential equations. The solution of differential equations using R is the main focus of this book. It is therefore intended for the practitioner, the student and the scientist, who wants to know how to use R for solving differential equations. However, it has been our goal that non-mathematicians should at least understand the basics of the methods, while obtaining entrance into the relevant literature that provides more mathematical background. Therefore, each chapter that deals with R examples is preceded by a chapter where the theory behind the numerical methods being used is introduced. In the sections that deal with the use of R for solving differential equations, we have taken examples from a variety of disciplines, including biology, chemistry, physics, pharmacokinetics. Many examples are well-known test examples, used frequently in the field of numerical analysis.

Differential equations -- Numerical solutions -- Data processing. --- Differential equations -- Numerical solutions. --- Maple (Computer file). --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Mathematical Statistics --- Differential equations --- R (Computer program language) --- Data processing. --- GNU-S (Computer program language) --- 517.91 Differential equations --- Mathematical statistics. --- Differential Equations. --- Differential equations, partial. --- Computer science --- Computer simulation. --- Statistics and Computing/Statistics Programs. --- Ordinary Differential Equations. --- Partial Differential Equations. --- Computational Mathematics and Numerical Analysis. --- Simulation and Modeling. --- Mathematics. --- Domain-specific programming languages --- Partial differential equations --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Mathematical models --- Simulation methods --- Model-integrated computing --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Statistical methods --- Statistics . --- Differential equations. --- Partial differential equations. --- Computer mathematics. --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics --- R (Computer program language).

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In shallow ecosystems, the microphytobenthos is considered as an important driver in modulating several biogeochemical processes through their activities. However, their inclusion in benthic ecosystem models is only discussed in a few studies. Here we implement a new model that extends a classic early diagenesis model (OMEXDIA) to include phosphorus dynamics and detailed MPB processes describing their complex physiological behavior. We investigated the role of microphytobenthos and other physical forcings on the biogeochemical dynamics within the sediment. This was done by considering four scenarios with varying degree of complexity involving light and tide effects. Our results show that inclusion of MPB can introduced fine-scale diurnal variability in several processes. Total mineralization was enhanced by 71.53% in the presence of MPB because of the input of fresh labile organic matter. This increased the depth of the oxic layer resulting in an increased coupled nitrification-denitrification process. Imposing the influence of tide effect resulted in high surface nutrient (ammonium, nitrate, phosphate) accumulation when the sediment was exposed, and that was quickly exchanged with the overlying water upon immersion. Thus, the sediment acts as a source of nutrient to the bottom water. The different scenarios explored in the model showed the complex behavior exhibited by MPB under dynamically changing environments which have significant biogeochemical ramifications.

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Partial differential equations --- Differential equations --- Artificial intelligence. Robotics. Simulation. Graphics --- Computer. Automation --- differentiaalvergelijkingen --- vormgeving --- informatica --- statistiek --- simulaties --- wiskunde