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"This textbook is an introduction to Scientific Computing, in which several numerical methods for the computer-based solution of certain classes of mathematical problems are illustrated. The authors show how to compute the zeros, the extrema, and the integrals of continuous functions, solve linear systems, approximate functions using polynomials and construct accurate approximations for the solution of ordinary and partial differential equations. To make the format concrete and appealing, the programming environments Matlab and Octave are adopted as faithful companions. The book contains the solutions to several problems posed in exercises and examples, often originating from important applications. At the end of each chapter, a specific section is devoted to subjects which were not addressed in the book and contains bibliographical references for a more comprehensive treatment of the material. From the review: " ... This carefully written textbook, the third English edition, contains substantial new developments on the numerical solution of differential equations. It is typeset in a two-color design and is written in a style suited for readers who have mathematics, natural sciences, computer sciences or economics as a background and who are interested in a well-organized introduction to the subject."

"The papers in this volume focus on the following topics: design optimization and inverse problems, numerical optimization techniques,efficient analysis and reanalysis techniques, sensitivity analysis and industrial applications. The conference EngOpt brings together engineers, applied mathematicians and computer scientists working on research, development and practical application of optimization methods in all engineering disciplines and applied sciences."

"Permasalahan optimasi merupakan permasalahan yang tidak asing ditemui dalam kehidu- pan sehari-hari. Dalam disiplin ilmu matematika, metode-metode untuk menyelesaikan masalah optimasi masih berkembang sampai saat ini. Salah satu metode numerik berbasis pencarian gradien yang memiliki kontribusi besar dalam bidang optimasi tak berkendala berskala besar adalah metode konjugat gradien. Metode ini terkenal atas keunggulannya karena memiliki formula iterasi yang sederhana dan kebutuhan penyimpanan yang relatif kecil. Seiring waktu, variasi-variasi baru dari metode konjugat gradien terus bermunculan. Hingga saat ini, usaha untuk membentuk metode konjugat gradien dengan properti konvergensi dan performa numerik yang lebih baik masih aktif menjadi topik penelitian. Pada skripsi ini, dibentuk suatu metode konjugat gradien hibrid baru yang merupakan modi kasi dari metode konjugat gradien Improved-Fletcher-Reeves (IFR) dan Improved-Dai-Yuan (IDY). Dengan beberapa kondisi dan asumsi, metode konjugat gradien hibrid IFR-IDY terbukti memenuhi kondisi descent dan konvergen secara global. Kemudian, berdasarkan 134 fungsi uji yang digunakan, metode konjugat gradien hibrid IFR-IDY juga terbukti memiliki performa numerik yang lebih e sien dari segi jumlah iterasi dan waktu komputasi dibandingkan metode konjugat gradien IFR dan metode konjugat gradien IDY. Lebih jauh lagi, metode konjugat gradien hibrid IFR-IDY juga terbukti efektif dalam menyelesaikan masalah seleksi portofolio saham.

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Optimization is a problem that we frequently encounter on a daily basis. In the discipline of mathematics, methods for solving optimization problems are still developing until today. One of the numerical methods based on gradient search that has made a major con- tribution to the eld of large-scale unconstrained optimization is the conjugate gradient method. This method is known for its advantages because it has a simple iteration formula and relatively small storage requirements. Over time, new variations of the conjugate gradient method continue to emerge. To this day, efforts to establish conjugate gradient methods with better convergence properties and numerical performance are still an active research topic. In this research, a new hybrid gradient conjugate method was created as a modi cation of the Improved-Fletcher-Reeves (IFR) and Improved-Dai-Yuan (IDY) conjugate gradient methods. With several conditions and assumptions, the IFR-IDY hybrid conjugate gradient method is proven to satisfy the descent condition and converge globally. In addition, based on the 134 test functions used, the IFR-IDY hybrid gradient conjugate method was also proven to have a more ef cient numerical performance in terms of the number of iterations and computing time compared to the IFR conjugate gradient method and the IDY conjugate gradient method. Furthermore, the IFR-IDY hybrid conjugate gradient method is also proven to be effective in solving stock portfolio selection problems."

"Potensi energi geotermal Indonesia merupakan yang terbesar di dunia, namun kini baru diutilisasi sekitar 4% dari potensi tersebut. Penelitian ini bertujuan mengoptimalkan penempatan sumur produksi geotermal di lapangan X agar risiko aktivitas pengembangan skema produksi dapat diminimalisasi. Pada penelitian ini dilakukan pemodelan dan simulasi reservoir dengan menggunakan data 3G (Geologi, Geofisika dan Geokimia) dari lapangan X dan data dari sumur yang telah ada. Dengan menggunakan TOUGH2, PETRASIM dan GeoSlicer-X, pemodelan forward yang mencakup adjustment dari litologi dan posisi sources dilakukan hingga model reservoir mencapai kondisi natural state. Data hasil simulasi reservoir kemudian diregresi menggunakan MATLAB serta dilakukan optimasi numerik guna mendapatkan titik-titik penempatan sumur produksi yang diajukan untuk penambahan kapasitas terpasang di lapangan X. Didapatkan hasil penelitian titik optimum penempatan sumur produksi pada koordinat x 3276 m dan y 4262 m dengan nilai entalpi spesifik maksimum 1529,9 kJ/kg; serta 6 titik penempatan sumur produksi dengan nilai entalpi spesifik 1500, 1450 dan 1400 kJ/kg. Dengan demikian, penambahan kapasitas terpasang dari skema produksi tambahan ini diestimasi dapat mencapai 43,5 MWe.

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Indonesia has the biggest estimated geothermal energy reserve in the world, but only 4% of that reserve currently utilized to generate electricity. The purpose of this research is to optimize the production well placements at X field to minimize the failure risk of production scheme development. In the research, reservoir modelling and simulation is conducted based on 3G (Geological, Geophysical and Geochemical) data and existing wells data. Forward modelling process, which covers the lithology and sources position adjustment, is executed with TOUGH2, PETRASIM and GeoSlicer-X to validate the reservoir model towards natural state condition.

Using MATLAB, the resulting data is regressed and used to numerically optimize the production well placement decision based on the fluid specific enthalpy. The new production scheme is proposed to further increase the installed capacity in X field. The final result is the optimal point of well placement; which is 3276 m in x coordinate and 4262 m in y coordinate with the maximum specific enthalpy value of 1529,9 kJ/kg and 6 (six) other points with specific enthalpy of 1500, 1450 or 1400 kJ/kg. Thus, the improvement of the installed capacity with the proposed production scheme is estimated to reach 43,5 MWe."