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"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. "

"ABSTRAKPenelitian ini bertujuan untuk mengetahui jenis tanah, korelasi parameter tanah dengan kedalaman, dan korelasi antar parameter tanah di wilayah DKI Jakarta berdasarkan hasil pengujian laboratorium di Laboratorium Mekanika Tanah Universitas Indonesia. Hasil penelitian ini menunjukan bahwa jenis tanah DKI Jakarta dominan terdiri dari 2 (dua) jenis tanah yaitu MH (lanau dengan plastisitas tinggi) dan SM (pasir berlanau). Berdasarkan korelasi parameter tanah dengan kedalaman di wilayah DKI Jakarta maka didapatkan kadar air (Wc) berkisar 19.7-133.5%, liquid limit (LL) berkisar 39-129%, plastic limit (PL) berkisar 28-77%, plasticity index (PI) berkisar 8-51.5%, density (γ) berkisar 12.8-18.5 kN/m3, specific gravity (Gs) berkisar 2.5-2.77, kohesi (c) berkisar 0-69 kN/m2, sudut geser berkisar 0-31°, angka pori (e0) berkisar 0.4-3.1, tegangan overburden (Po) berkisar 15-144 kPa, tegangan pre-consolidated (Pc) berkisar 37-358 kPa, indeks kompresi (Cc) berkisar 0.09-1.51, dan indeks pemampatan kembali (Cr) berkisar 0.01-0.32. Berdasarkan korelasi index properties dan engineering properties, yaitu korelasi antara Cc dengan PI, Cc dengan LL, Cc dengan e0, Cc dengan Wc, e0 dengan Wc, dan e0 dengan γ, menghasilkan koefisien korelasi dengan tingkat hubungan kuat, kecuali korelasi antara Cc dengan PI dan Cc dengan LL pada Kelompok 1 dan Kelompok 2 kurang dapat diandalkan karena memiliki koefisien korelasi dengan tingkat hubungan rendah.

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ABSTRACTThis study aims to determine the type of soil, the correlation of soil parameters with depth, and the correlation between soil parameters in the DKI Jakarta region based on the results of laboratory testing at the University of Indonesia's Laboratory of Soil Mechanics. Statistical data processing uses Microsoft Excel to graph, linear equations, calculation of the coefficient of variance (COV) and correlation coefficients. The results of this study indicate that the type of soil in the DKI Jakarta area is dominant consisting of 2 (two) types of soil, namely MH (silt with high plasticity) and SM (silty sand) with high plasticity. Based on the correlation of soil parameters with depth in the DKI Jakarta area, the Wc was 19.7-133.5%, LL was 39-129%, PL was 28-77%, PI was 8-51.5%, γ was 12.8-18.5 kN/m3, Gs was 2.5-2.77, c was 0-69 kN/m2, friction angles was 0-31°, e0 was 0.4-3.1, Po was 15-144kPa, Pc was 37-358kPa, Cc was 0.09-1.51, and Cr was 0.01-0.32. Based on correlation index properties and engineering properties, the correlation between Cc and PI, Cc with LL, Cc with e0, Cc with Wc, e0 with Wc, and e0 with γ, produces a correlation coefficient with a strong level of correlation."

"This textbook presents basic numerical methods and applies them to a large variety of physical models in multiple computer experiments. Classical algorithms and more recent methods are explained. Partial differential equations are treated generally comparing important methods, and equations of motion are solved by a large number of simple as well as more sophisticated methods. Several modern algorithms for quantum wavepacket motion are compared. The first part of the book discusses the basic numerical methods, while the second part simulates classical and quantum systems. Simple but non-trivial examples from a broad range of physical topics offer readers insights into the numerical treatment but also the simulated problems. Rotational motion is studied in detail, as are simple quantum systems. A two-level system in an external field demonstrates elementary principles from quantum optics and simulation of a quantum bit. Principles of molecular dynamics are shown. Modern boundary element methods are presented in addition to standard methods, and waves and diffusion processes are simulated comparing the stability and efficiency of different methods. A large number of computer experiments is provided, which can be tried out even by readers with no programming skills. Exercises in the applets complete the pedagogical treatment in the book. In the third edition Monte Carlo methods and random number generation have been updated taking recent developments into account. Krylov-space methods for eigenvalue problems are discussed in much more detail. The wavelet transformation method has been included as well as simple applications to continuum mechanics and convection-diffusion problems. Lastly, elementary quantum many-body problems demonstrate the application of variational and Monte-Carlo methods. "