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"Untuk memperoleh hasil yang optimal dalam reaksi oksidasi parsial Metana, perlu dicari rasio yang tepat antara Oksigen (O2) dan Metana (CH4) sebagai reaktan (rasio reaktan). Selain itu perlu dianalisa kemungkinan terbentuknya senyawa Karbon dalam bentuk padat. Analisa terhadap reaksi oksidasi parsial Metana dilakukan melalui pendekatan model matematika berupa Sistem Persamaan Non Linier (SPNL) yang dalam penyelesaiannya digunakan Metode Broyden. Hasil komputasi yang diperoleh dari penerapan Metode Broyden adalah bahwa tidak terbentuk senyawa Karbon dalam bentuk padat dan rasio reaktan sebesar 0.5767154 dapat memberikan hasil yang optimal. "

"For those interested in advanced study and research in nonlinear partial differential equations and nonlinear wave phenomena. Updated modern examples of applications are chosen from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation."

"The second edition, now republished in SIAM's Classics in Applied Mathematics series, provides a rigorous mathematical analysis of the behavior of nonlinear control systems under a variety of situations. It develops nonlinear generalizations of a large number of techniques and methods widely used in linear control theory. The book contains three extensive chapters devoted to the key topics of Lyapunov stability, input-output stability, and the treatment of differential geometric control theory. In addition, it includes valuable reference material in these chapters that is unavailable elsewhere. The text also features a large number of problems that allow readers to test their understanding of the subject matter and self-contained sections and chapters that allow readers to focus easily on a particular topic."

"Pencarian solusi pada sistem persamaan non-linier dapat dilakukan dengan cara langsung maupun tidak langsung. Salah satu cara tidak langsung yang digunakan adalah metode numerik. Metode Newton merupakan salah satu metode numerik untuk mencari solusi pada sistem persamaan non-linier. Metode Newton-like merupakan improvisasi dari Metode Newton, yang memiliki sebuah parameter berupa bilangan real yang berperan sebagai pengontrol kecepatan konvergensinya. Metode ini bersifat konvergen kuadratik, serta dianggap lebih baik daripada metode Newton untuk matriks Jacobi yang mendekati singular pada vektor inisial. Simulasi numerik dilakukan pada Metode Newton dan Newton-like dengan menggunakan lima sistem persamaan non-linier, yang masing-masingnya menggunakan empat nilai real untuk parameter pada Newton-like. Vektor inisial didapat dengan membuat nilai determinan Matriks Jacobi pada sistem persamaan non-linier mendekati nol. Berdasarkan simulasi numerik yang telah dilakukan, metode Newton-like secara umum lebih cepat konvergen daripada metode Newton. Kemudian, dari masing-masing sistem dapat ditentukan ada atau tidaknya sebuah nilai parameter optimal pada Metode Newton-like.

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Finding solutions on systems of non linear equations can be done by direct or indirect way. One of the inderect way is numerical methods. Newton method is one of the numerical methods to find solutions on systems of non linear equations. Newton like is an improvement of Newton method, which has a real parameter as the convergence speed regulator. This method is quadratic convergent, and considered better than Newton for Jacobian that is close to singular on initial vector.

Numerical simulations are performed on Newton and Newton like using five systems of non linear equations, which each system using four real values for the parameter on Newton like. The initial vector is obtained by making the determinant of Jacobian on systems close to zero. Newton like are generally faster than Newton Method. Later, from each system can be determined whether or not an optimal value on Newton like Method. "

"Besarnya kebutuhan akan kemasan kayu dalam kegiatan perdagangan menuntut produsen kemasan kayu untuk mengembangkan sistem penjadwalan produksi yang optimal agar dapat memenuhi permintaan pasar. Penelitian ini membahas optimasi penjadwalan produksi kemasan kayu, khususnya pallet, dengan system job shop melalui penerapan algoritma Differential Evolution. Prinsip algoritma DE sesuai dengan analogi evolusi biologi yang terdiri dari proses inisialisasi populasi, proses mutasi, proses pindah silang, dan proses seleksi. Tujuan dari penelitian ini adalah untuk meminimumkan total biaya (dalam satutan waktu) yang timbul sebagai akibat dari keterlambatan dalam proses produksi kemasan kayu, khususnya pallet yang dipergunakan untuk mengemas barang-barang ekspor. Penelitian dilakukan melalui studi kasus dengan mengamati proses produksi pallet pada suatu produsen pallet. Hasil dari penelitian ini adalah diperolehnya usulan penjadwalan produksi dengan penurunan total biaya keterlambatan sebesar 25,22%, (dari 23590 menit menjadi 17640 menit) serta penurunan pada kriteria lainnya seperti jumlah pesanan yang terlambat, total waktu keterlambatan, dan waktu penyelesaian. Simulasi penambahan kapasitas menunjukkan bahwa penambahan jumlah mesin pada stasiun serut dan potong dapat menghilangkan keterlambatan dan meningkatkan output hingga 95%.

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The ever increasing need of wooden packaging , whether for international as well as inter-islands transportation of traded goods, has required the producers of wooden packaging to develop an optimized production scheduling system to fulfill the market demand. This research studies the optimization of the job shop production scheduling system of wooden packaging, particularly pallet, through the application of the Differential Evolution (DE) algorithm. The principles of the DE algorithm is in line with the biological evolution analogy which consists of the initialization of population, mutation, crossover, and selection processes. The DE algorithm has some excellent features namely the concept is simple, easy to apply, quick in producing solutions, and robust. The objektif of this research is to minimize the total cost (in time unit) resulting from the delay in the production process of wooden packaging, particularly pallet.

This research is a case-study which is carried-out by observing pallet production process at a wooden packaging manufacturer. The company produces wood packaging, mainly pallet, which are used for the packaging of exported goods. This research leads to a recommendation on the wooden packaging production schedule with more efficient cost. The total cost resulting from the delay in the production is reduced by 25,22% (from 23590 minutes to 17640 minutes). There are also reductions in the total of tardy job, total of tardiness, and makespan. A simulation of work station capacity upgrade also shows that the addition of the number of machineries in planing and sawing station will eliminate delay and increase output up to 95%."

"This book shows how to apply theoretical mathematical models to unravel the mechanisms involved in processes found in mathematical physics and the biosciences. It is a unique collection of abstract methods that deploy nonlinear partial differential equations. "

"This book presents recent results on nonlinear parabolic-hyperbolic coupled systems such as the compressible navier-stokes equations, and liquid crystal system. It summarizes recently published research by the authors and their collaborators, but also includes new and unpublished material. All models under consideration are built on compressible equations and liquid crystal systems. This type of partial differential equations arises not only in many fields of mathematics, but also in other branches of science such as physics, fluid dynamics and material science."