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"Mengukur tingkat polusi udara berarti mengukur tingkat konsentrasipolutan dalam udara. Pengukuran tersebut dilakukan dengan pendekatan modelmatematika sederhana berupa Persamaan Diferensial Parsial Order Dua.Berdasarkan model sederhana tersebut yang diperoleh dari Model DanishEulerian, akan dicari solusi eksaknya (jika ada) dan solusi numeriknya. Adapunmetode eksak yang digunakan adalah Metode Transformasi Laplace pada ruang.Sedangkan untuk memperoleh solusi numeriknya, digunakan Metode CrankNicolson."

"A concise survey of the current state of knowledge in 1972 about solving elliptic boundary-value eigenvalue problems with the help of a computer. This volume provides a case study in scientific computing -- the art of utilizing physical intuition, mathematical theorems and algorithms, and modern computer technology to construct and explore realistic models of problems arising in the natural sciences and engineering."

"Permodelan turbulen yang digunakan adalah model aljabar sederhana ( model not persamaan ), yang disajikan dalam bentuk PDE. Persamaan - persamaan differensial yang diselesaikan adalah persamaan kontinuitas, momentum dan energi. Kemudian dengan metoda Beda Hingga secara implisit, persamaan - persamaan tersebut diubah kedalam persamaan numerik dan diselesaikan dengan metoda TDMA ( Tridiagonal Matrices Algorithm ) secara numerik. Hasil akhir dari penyelesaian Sistem Persamaan Differensial akan diperoleh distribusi temperatur udara pada penampang melintang dengan jarak 0,61 m; 1,22 m dan 1,83 m dari sisi masuk-ruang annulus. Dari hasil penelitian ini dapat dinyatakan bahwa kesesuaian antara data numerik dan data eksperimen yang cukup baik terjadi pada jarak dari sisi masuk ruang annulus sebesar 1,22 m. Untuk penelitian selanjutnya dengan tema yang sama, sebaiknya hanya dilakukan pada jarak dari sisi masuk ruang annulus 1,22 m saja, meskipun metoda yang digunakan berbeda.

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The mathematical model provides differential equations for : continuity, momentum, energy. The simultaneous solution of these equations by means of a finite difference solution in the form of implicit equation systems.By TDMA ( Tridiagonal Matrices Algorithm ), we will get the numerical solutions. The result of this research, we can describe temperature distribution of air in the cross section at axial distances 0.61m, 1.22 m and 1.83 m from annular space inlet. The comparison between numerical results and experimental data shows a good result, especially at distance 1.22 m or the fully developed region of the air flow. Suggestion, the next research do only at distance 1.22 m from annular space inlet, although use different method."

"Mumby dkk. (2008) membuat model matematika terumbu karang dalam suatu persamaan diferensial biasa nonlinier. Model ini menggambarkan interaksi antara makro alga, karang, dan alga turf yang merupakan organisme yang menutupi dasar laut terumbu. Salah satu asumsi modelnya disebutkan bahwa grazing terhadap makro alga dapat menyebabkan tumbuhnya alga turf. Beberapa tahun berikutnya, Li dkk. (2014) mengembangkan model terumbu karang Mumby dengan adanya waktu tunda. Hal tersebut didasarkan pada fakta bahwa dibutuhkan waktu yang lama untuk alga turf tumbuh setelah makro alga dimakan. Tujuan dari skripsi ini ialah memberikan perbandingan kestabilan titik kesetimbangan pada kedua model beserta bifurkasi yang terjadi.

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Mumby et al. (2008) constructed a mathematical model of coral reef with nonlinear ordinary differential equation. This model described interaction between macro algae, coral and algal turf which are organism who live in seabed of reef. One assumption of model mentioned that grazing on macro algae giving rise to algal turf. The next few years, Li et al. (2014) extended Mumby?s coral reef model with time delay. It is based from the fact that it takes a long period of time for algal turf to arise after macro algae are grazed. The aim of this undergraduate thesis is to present comparison of stability of the equilibrium points in both model and the occurance of bifurcation."

"This book primarily focuses on rigorous mathematical formulation and treatment of static problems arising in continuum mechanics of solids at large or small strains, as well as their various evolutionary variants, including thermodynamics. As such, the theory of boundary- or initial-boundary-value problems for linear, quasilinear elliptic, parabolic or hyperbolic partial differential equations is the main underlying mathematical tool, along with the calculus of variations. Modern concepts of these disciplines as weak solutions, polyconvexity, quasiconvexity, nonsimple materials, materials with various rheologies or with internal variables are exploited."

"The issue of regularity has played a central role in the theory of Partial Differential Equations almost since its inception, and despite the tremendous advances made it still remains a very fruitful research field. The course aimed to show the deep connections between these topics and to open new research directions through the contributions of leading experts in all of these fields."

"Model-model Persamaan Diferensial Stokastik (PDS) memiliki peranan yang sangat penting di berbagai bidang industri, misalnya ekonomi, keuangan, biologi, kimia, epidemiologi, juga mikroelektronik (Higham D. J., 2001). Metode numerik seringkali digunakan untuk mengaproksimasi solusi dari suatu model PDS, sehingga dibutuhkan suatu proses komputasi untuk memperoleh solusi dari suatu model PDS tersebut. Model-model PDS biasanya melibatkan data dalam jumlah besar ataupun proses komputasi yang banyak, sehingga berdampak pada waktu komputasi yang semakin lama. Untuk mempercepat waktu komputasi, maka diterapkan komputasi paralel. Komputasi paralel adalah salah satu teknik melakukan komputasi secara bersamaan dengan memanfaatkan beberapa komputer/prosesor pada suatu waktu tertentu.Dalam skripsi ini diberikan algoritma paralel untuk mengaproksimasi solusi dari suatu model PDS. Algoritma-algoritma ini diimplementasikan dalam program yang dijalankan pada mesin multicore dengan MATLAB dan Parallel Computing Toolbox (versi trial). Diberikan juga kinerja algoritma paralel yang diukur dengan speed up dan efisiensi paralel.Stochastic Differential Equations (SDEs) models play a prominent role in a range of application areas, including biology, chemistry, epidemiology, mechanics, microelectronics, economics, and finance (Higham D. J., 2001). Numerical method is usually used to get an approximate solution of SDEs models which often involve huge data or many computation steps, hence need more computation time. Parallel computing is an alternative that can reduce the computation time.

This skripsi discuss some parallel techniques to solve SDEs problems especially in finance models. The parallel techniques is designed to utilize several processors simultaneously. In this case the algorithms run on multicore machine with MATLAB and Parallel Computing Toolbox (trial version). Parallel perfomance of the algorithms are also given which compared the speed up and efficiency of several parallel techniques."

"While the prediction of observations is a forward problem, the use of actual observations to infer the properties of a model is an inverse problem. Inverse problems are difficult because they may not have a unique solution. The description of uncertainties plays a central role in the theory, which is based on probability theory. This book proposes a general approach that is valid for linear as well as for nonlinear problems. The philosophy is essentially probabilistic and allows the reader to understand the basic difficulties appearing in the resolution of inverse problems. The book attempts to explain how a method of acquisition of information can be applied to actual real-world problems, and many of the arguments are heuristic."