A Trigonometrically Fitted Block Method for Solving Oscillatory Second-Order Initial Value Problems and Hamiltonian Systems

In this paper, we present a block hybrid trigonometrically fitted Runge-Kutta-Nyström method (BHTRKNM), whose coefficients are functions of the frequency and the step-size for directly solving general second-order initial value problems (IVPs), including Hamiltonian systems such as the energy conserving equations and systems arising from the semidiscretization of partial differential equations (PDEs). Four discrete hybrid formulas used to formulate the BHTRKNM are provided by a continuous one-step hybrid trigonometrically fitted method with an off-grid point. We implement BHTRKNM in a block-by-block fashion; in this way, the method does not suffer from the disadvantages of requiring starting values and predictors which are inherent in predictor-corrector methods. The stability property of the BHTRKNM is discussed and the performance of the method is demonstrated on some numerical examples to show accuracy and efficiency advantages

Pengaruh Penerapan Etika Kerja Islam Dan Pelayanan Prima Terhadap Kinerja Karyawan Bank Syariah Indonesia KCP Cirebon-Ciledug

REYMITHA JATOR HIDAYAT. NIM: 1708203049. “PENGARUH PENERAPAN ETIKA KERJA ISLAM DAN PELAYANAN PRIMA TERHADAP KINERJA KARYAWAN BANK SYARIAH INDONESIA KCP CIREBON-CILEDUG” Berkembangnya suatu organisasi perusahaan sangat bergantung dari bagaimana seluruh karyawan yang bekerja dalam organisasi tersebut. Semakin baik kinerja yang diberikan karyawan maka akan semakin baik pula kinerja organisasi tersebut. Perbankan syariah merupakan salah satu organisasi dimana karyawan sangat berpengaruh terhadap keberlangsungan hidup perusahaan tersebut. Karena peran seorang karyawan dalam perbankan sangat penting dalam menciptakan citra perusahaan. Kinerja seorang karyawan merupakan kualitas yang berarti hasil pekerjaan yang dicapai oleh seorang pekerja yang dapat dibuktikan dan diukur sesuai standar yang telah ditentukan. Faktor-faktor yang dapat mempengaruhi kinerja karyawan diantaranya kompensasi, lingkungan kerja, budaya organisasi, kepemimpinan, motivasi kerja, disiplin kerja, kepuasan kerja dan komunikasi. Bank Syariah Indonesia sendiri merupakan organisasi yang mempunyai aturan ketat terkait etika dan pelayanan dalam bekerja mereka di perusahaan. Oleh karena itu, perlu diteliti apakah etika kerja islam dan pelayanan prima berpengaruh terhadap kinerja karyawan. Rumusan masalah dalam penelitian ini yaitu: 1. Bagaimana pengaruh penerapan etika kerja islam terhadap kinerja karyawan Bank Syariah Indonesia KCP Cirebon-Ciledug, 2. Bagaimana pengaruh penerapan pelayanan prima terhadap kinerja karyawan Bank Syariah Indonesia KCP Cirebon-Ciledug, 3. Bagaimana pengaruh penerapan etika kerja islam dan pelayanan prima terhadap kinerja karyawan Bank Syariah Indonesia KCP Cirebon-Ciledug. Teknik analisis data yang digunakan dalam penelitian ini yaitu analisis deskriptif, analisis statistik berupa uji validitas, uji reliabilitas, uji asumsi klasik, uji regresi linear berganda, uji hipotesis berupa uji t (parsial) dan uji F (simultan), serta uji koefisien determinasi (R2) dengan menggunakan SPSS Statistik Versi 23. Hasil penelitian ini menunjukan bahwa terdapat pengaruh signifkan antara etika kerja islam terhadap kinerja karyawan sebesar 69,97% serta tidak terdapat pengaruh signifikan antara pelayanan prima terhadap kinerja karyawan dengan hasil 00,50%. Secara simultan, etika kerja islam dan pelayanan prima bersamasama mempengaruhi kinerja karyawan Bank Syariah Indonesia KCP Cirebon- Ciledug dengan kontribusi sebesar 70,4%. Kata Kunci: Etika Kerja Islam, Pelayanan Prima, Kinerja Karyawa

Solving the Telegraph and Oscillatory Differential Equations by a Block Hybrid Trigonometrically Fitted Algorithm

We propose a block hybrid trigonometrically fitted (BHT) method, whose coefficients are functions of the frequency and the step-size for directly solving general second-order initial value problems (IVPs), including systems arising from the semidiscretization of hyperbolic Partial Differential Equations (PDEs), such as the Telegraph equation. The BHT is formulated from eight discrete hybrid formulas which are provided by a continuous two-step hybrid trigonometrically fitted method with two off-grid points. The BHT is implemented in a block-by-block fashion; in this way, the method does not suffer from the disadvantages of requiring starting values and predictors which are inherent in predictor-corrector methods. The stability property of the BHT is discussed and the performance of the method is demonstrated on some numerical examples to show accuracy and efficiency advantages

Heat transfer study of convective fin with temperature-dependent internal heat generation by hybrid block method

Purpose: In this study, an implicit one‐step hybrid block method using two off‐step points involving the presence of a third derivative for solving second‐order boundary value problems are subjected to Dirichlet‐mixed conditions. Methodology: To derive this method, the approximate power series solution is interpolated at urn:x-wiley:10992871:media:htj21428:htj21428-math-0001 while its second and third derivatives are collocated at all points urn:x-wiley:10992871:media:htj21428:htj21428-math-0002 on the integrated interval of approximation. Findings: The new derived method not only performs better compared with the existing methods when solving the same problems but also obtains better properties of the numerical method. Afterward, the proposed method is applied to solve the problem of a convective fin with temperature‐dependent internal heat generation. The effects of various physical parameters on temperature distribution are also examined

Trigonometric symmetric boundary value method for oscillating solutions including the sine-Gordon and Poisson equations

We construct a continuous linear multistep method with trigonometric coefficients from which a symmetric main method as well as additional methods are reproduced. The main and additional methods whose coefficients depend on the frequency and step length are then applied as a trigonometric symmetric boundary value method (SBVM) to solve systems of second-order initial and boundary value problems of the form $\mathbf y^{\prime \prime } = f( x,\,y)$ without first reducing the ordinary differential equation into an equivalent first-order system. Moreover, the method is successfully applied to solve hyperbolic and elliptic partial differential equations, such as the sine-Gordon and the Poisson equations. The stability property of the SBVM is discussed and numerical experiments are performed to show the accuracy of the method

A Family of Functionally-Fitted Third Derivative Block Falkner Methods for Solving Second-Order Initial-Value Problems with Oscillating Solutions.

[EN]One of the well-known schemes for the direct numerical integration of second-order initial-value problems is due to Falkner. This paper focuses on the construction of a family of adapted block Falkner methods which are frequency dependent for the direct numerical solution of second-order initial value problems with oscillatory solutions. The techniques of collocation and interpolation are adopted here to derive the new methods. The study of the properties of the proposed adapted block Falkner methods reveals that they are consistent and zero-stable, and thus, convergent. Furthermore, the stability analysis and the algebraic order conditions of the proposed methods are established. As may be seen from the numerical results, the resulting family is efficient and competitive compared to some recent methods in the literature

Efficient k-Step Linear Block Methods to Solve Second Order Initial Value Problems Directly.

[EN]There are dozens of block methods in literature intended for solving second order initial-value problems. This article aimed at the analysis of the efficiency of -step block methods for directly solving general second-order initial-value problems. Each of these methods consists of a set of 2-multi-step formulas (although we will see that this number can be reduced to +1 in case of a special equation) that provides approximate solutions at grid points at once. The usual way to obtain these formulas is by using collocation and interpolation at different points, which are not all necessarily in the mesh (it may also be considered intra-step or off-step points). An important issue is that for each , all of them are essentially the same method, although they can adopt different formulations. Nevertheless, the performance of those formulations is not the same. The analysis of the methods presented give some clues as how to select the most appropriate ones in terms of computational efficiency. The numerical experiments show that using the proposed formulations, the computing time can be reduced to less than half

A 14-Order Hybrid Block Method in Variable Step-Size Mode for Solving Second-Order Initial Value Problems.

[EN]The search for efficient higher order methods is a constant goal in numerical analysis. In this paper, a higher order two-step hybrid block method is presented to directly solve second-order initial value problems in ordinary differential equations. In addition to the higher order, the proposed method has been formulated in variable step-size mode to extract its best performance. Comparisons with other methods in the literature show the good accuracy it can provide. Theoretical aspects such as linear stability and convergence analysis are also discussed

Block Hybrid Method for the Numerical solution of Fourth order Boundary Value Problems.

[EN]A linear Multistep Block Hybrid Method with four off-grid points is presented for the direct approximation of the solution of fourth order Boundary Value Problems. Multiple Finite Difference formulas are derived and grouped into a unique block to form a numerical integrator to solve directly the fourth order problem, without the need to reduce it previously to a first-order system. The convergence of the proposed method is discussed. The superiority of this method over existing methods is established numerically considering different problems that have appeared in the literature