An Analytical Solution Of 1-D Pseudo Homoneneous Model For Oxidation Reaction Using Homotopy Perturbation Method

In this paper, we propose an analytical solution of convective-diffusion equation that derived from an oxidation reaction in a chemical reactor. Here, concentration of feed gas as dependent variable. In this study, the reaction are assumed to be a one-dimensional pseudo homogeneous model and it is evaluated at a certain reaction rate. By rescaling process, the nonlinear term of the reaction rate can be approximated by a linear term, resulting a linear convective-diffusion equation with an initial condition and a set of boundary conditions. Here, we present an analytic solution of the initial condition and the boundary conditions using the homotopy perturbation method. The results show that at the end of the reactor, the solution is in agreement with numerical solution of the initial and boundary conditions

Application of singular spectrum analysis (SSA) method on forecasting train passengers data in sumatera

A time series is a series of observations of a variable that is collected, recorded, or observed over a period of time in sequence. Singular Spectrum Analysis is a powerful method to analyze time series data by decomposing the original time series data into several small components that can be identified, such as trend, periodic, and noise components. One of the datasets that can be used is data on the number of train passengers in Sumatera in 2013–2022. In this study, the Singular Spectrum Analysis method is used to forecast the number of train passengers in Sumatera in 2013–2022. The best Singular Spectrum Analysis model in this study was obtained at a window length of 22 and a number of groups of 8, with a MAPE value of 19.55%

Variational homotopy perturbation method for solving systems of homogeneous linear and nonlinear partial differential equations

The variational homotopy perturbation method is developed by combining variational iteration method and homotopy perturbation method. Variational iteration method has an efficient process in solving a wide variety of equations and systems of equations. Meanwhile, homotopy perturbation method yields a very rapid convergence of the solution series in most cases. The developed method, variational homotopy perturbation method, took full advantage of both methods. In this study, we described an application of the variational homotopy perturbation method to solve systems of homogeneous partial differential equations. Here we consider some initial value problems of homogeneous partial differential equation systems with two and three variables. The results show that the obtained solution using this method was in agreement with the solution using the homotopy analysis method and variational iteration method, which prove the validity of the variational homotopy perturbation method when applied to systems of partial differential equations

IMPLEMENTASI METODE BACKPROPAGATION NEURAL NETWORK DALAM MERAMALKAN TINGKAT INFLASI DI INDONESIA

Peramalan  merupakan upaya dalam memperkirakan sesuatu di masa depan berdasarkan pada pola data atau informasi di masa lalu. Autoregressive Integrated Moving Average (ARIMA), Exponential Smoothing, dan Seasonal Autoregressive Integrated Moving Average (SARIMA) merupakan beberapa metode yang sering digunakan dalam peramalan data deret waktu. Namun, metode tersebut memiliki kelemahan yaitu data yang digunakan harus stasioner serta akurasi yang dihasilkan kurang baik. Untuk mengatasi kelemahan tersebut, peneliti banyak yang menerapkan metode Jaringan Syaraf Tiruan salah satunya Backpropagation Neural Network. Metode Backpropagation Neural Network sangat baik digunakan dalam peramalan bidang ekonomi. Masalah ekonomi di Indonesia yang sampai saat ini masih menjadi permasalahan besar adalah inflasi. Dalam kajian ini, dilakukan peramalan inflasi di Indonesia menggunakan data inflasi periode Januari 2000 hingga Oktober 2022. Hasil yang diperoleh menunjukan pembagian data terbaik yaitu 50% training dan 50% testing dengan menggunakan fungsi aktivasi sigmoid biner didapatkan arsitektur terbaik yaitu 12-21-1 dengan nilai Mean Square Error (MSE) pada tahapan training sebesar 0,00067535 dan pada tahapan testing yaitu 0,0767. Setelah dilakukan peramalan, diperoleh bahwa inflasi tertinggi terjadi pada bulan Oktober 2023 sebesar 0,5579 serta peramalan inflasi terkecil terjadi pada Februari 2023 sebesar 0,203

IMPLEMENTATION OF ARTIFICIAL NEURAL NETWORK WITH BACKPROPAGATION ALGORITHM FOR RATING CLASSIFICATION ON SALES OF BLACKMORES IN TOKOPEDIA

The rating assessment classification contains feedback from consumers, which is given in the form of stars which aims to assess a product. However, the amount of data in the classification process often have differences in each class or is called an imbalanced dataset. These problems can affect the classification results. An imbalanced dataset can be overcome by applying random oversampling. To classify the rating assessment, this study proposes the Neural network method, which has a good accuracy level with the backpropagation algorithm and applies random oversampling to overcome the unbalanced amount of data. The results indicate that the neural network method with the backpropagation algorithm can classify the available data with an accuracy level of 85%. The application of resampling data using random oversampling and determining the amount of distribution of training data, testing data, number of epochs and the correct number of batch sizes affect the results obtained

A Singular Perturbation Problem for Steady State Conversion of Methane Oxidation in a Reverse Flow Reactor

The governing equations describing methane oxidation in a reverse flow reactor are given by a set of convective-diffusion equations with a nonlinear reaction term, where temperature and methane conversion are dependent variables. In this study, the process is assumed to be a one-dimensional pseudohomogeneous model and takes place with a certain reaction rate in which thewhole process ofthereactor is still workable. Thus, the reaction rate can proceed at a fixed temperature. Under these conditions, we can restrict ourselves to solving the equations for the conversion only. From the available data, it turns out that the ratio of the diffusion term to the reaction term is small. Hence, this ratio is considered as a small parameter in our model and this leads to a singular perturbation problem. Numerical difficulties will be found in the vicinity of a small parameter in front of a higher order term. Here, we present an analytical solutionby means of matched asymptotic expansions. The result shows that, up to and including the first order of approximation, the solution is in agreement with the exact and numerical solutions of the boundary value problem

Design Optimization of Propellant Grain and Nozzle Contour to Improve Performance of Solid Rocket Propulsion

A rocket is a spacecraft, guided missile, or flying vehicle that boosted by a chemical reaction resulting from the combustion of propellant in the rocket motor. One of the essential parameters in the development of rocket motors is design optimization to improve the propulsion performance of the rocket. Increasing the propulsion performance of the rocket will increase the flight performance of the rocket, in terms of its maximum range or the altitude of the rocket trajectory. This study examined the determination of the design parameter values of a rocket motor by looking at it as an optimization problem with constraints. The problem studied was limited to the case of the second-stage rocket motor. A genetic algorithm was used to solve the resulting optimization problem of propellant grain configuration cases and a characteristic method for designing the bell nozzle. The results obtained indicated an increase in total impulse by 10% compared to the results before optimization

Design Optimization of Propellant Grain and Nozzle Contour to Improve Performance of Solid Rocket Propulsion

A rocket is a spacecraft, guided missile, or flying vehicle that boosted by a chemical reaction resulting from the combustion of propellant in the rocket motor. One of the essential parameters in the development of rocket motors is design optimization to improve the propulsion performance of the rocket. Increasing the propulsion performance of the rocket will increase the flight performance of the rocket, in terms of its maximum range or the altitude of the rocket trajectory. This study examined the determination of the design parameter values of a rocket motor by looking at it as an optimization problem with constraints. The problem studied was limited to the case of the second-stage rocket motor. A genetic algorithm was used to solve the resulting optimization problem of propellant grain configuration cases and a characteristic method for designing the bell nozzle. The results obtained indicated an increase in total impulse by 10% compared to the results before optimization

Computational Mathematics: Solving Dual Fully Fuzzy Nonlinear Matrix Equations Numerically using Broyden’s Method

Fuzzy numbers have many applications in various mathematical models in both linear and nonlinear forms. In the form of a nonlinear system, fuzzy nonlinear equations can be constructed in the form of matrix equations. Unfortunately, the matrix equations used to solve the problem of dual fully fuzzy nonlinear systems are still relatively few found in the publication of research results. This article attempts to solve a dual fully fuzzy nonlinear equation system involving triangular fuzzy numbers using Broyden’s method. This article provides the pseudocode algorithm and the implementation of the algorithm into the MATLAB program for the iteration process to be carried out quickly and easily. The performance of the given algorithm is the fastest in finding system solutions and provides a minimum error value

Simulasi Jumlah Klaim Agregasi Berdistribusi Poisson Dengan Besar Klaim Berdistribusi Gamma dan Rayleigh

A claim is a transfer of risk from the insured to the guarantor. Claims that occur individually are called individual claims, whereas collections of individual claims are called aggregation claims in a single period of vehicle insurance. Aggregation claims consist of a pattern of the number and amount (nominal value) of individual claims, so that the model of aggregation claims is formed from each distribution of the number and amount of claims. The distribution of claims is based on the probability density function and the cumulative density function. One method that can be used to obtain a claim aggregation model is to use convolution, which is by combining the distribution of the number of claims and the distribution of the amount of claims so that the expected value can be obtained to predict the value of pure premiums. In this paper, aggregation claim modeling will be carried out with the number of claims distributed Poisson and the amount of claims distributed Gamma. As comparison, we compare it with claim amount distributed Rayleigh. By using VaR (value at risk) and MSE (Mean Square Error) indicators, the results of the analysis show that the Rayleigh distribution is better used for distributing data that has extreme values