Study on Numerical Solutions to Hyperbolic Partial Differential Equations Based on the Convolutional Neural Network Model

This manuscript is concerning to investigate numerical solutions for different classesincluding parabolic, elliptic and hyperbolic partial differential equations of arbitrary order(PDEs). The proposed technique depends on some operational matrices of fractional order differentiation and integration. To compute the mentioned operational matrices, we apply shifted Jacobi polynomials in two dimension. Thank to these matrices, we convert the (PDE) under consideration to an algebraic equation which is can be easily solved for unknown coefficient matrix required for the numerical solution. The proposed method is very efficient and need no discretization of the data for the proposed (PDE). The approximate solution obtain via this method is highly accurate and the computation is easy. The proposed method is supported by solving various examples from well known articles.

Download Full-text

Steady Gravity Flow of Frictional-Cohesive Solids in Converging Channels

Journal of Applied Mechanics ◽

10.1115/1.3629571 ◽

1964 ◽

Vol 31 (1) ◽

pp. 5-11 ◽

Cited By ~ 72

Author(s):

A. W. Jenike

Keyword(s):

Partial Differential Equations ◽

Stress Field ◽

Differential Equations ◽

Radial Stress ◽

Numerical Solutions ◽

Yield Function ◽

Hyperbolic Partial Differential Equations ◽

Stress Fields ◽

Special Importance ◽

Partial Differential

Frictional-cohesive solids such as soil, ores, chemicals, sugar, flour are regarded as plastic and represented by the Jenike-Shield yield function [1] during steady flow. The stress-strain rate relations are based on isotropy, continuity, and a one-to-one dependence of density on the major pressure. In plane strain and in axial symmetry the stress field requires the solution of a system of two hyperbolic partial differential equations. The velocity field can then be computed by solving another system of two linear homogeneous partial differential equations of the hyperbolic type. In straight conical channels, a particular stress field called the “radial stress field” assumes a special importance because evidence has been presented elsewhere that all general fields tend to approach the radial stress fields in the vicinity of the vertex. Examples of numerical solutions of radial stress fields are given.

Download Full-text

KLASIFIKASI CITRA GENUS PANTHERA MENGGUNAKAN METODE CONVOLUTIONAL NEURAL NETWORK (CNN)

Jurnal Ilmiah Informatika Komputer ◽

10.35760/ik.2019.v24i3.2364 ◽

2019 ◽

Vol 24 (3) ◽

pp. 220-228

Author(s):

Gusti Alfahmi Anwar ◽

Desti Riminarsih

Keyword(s):

Neural Network ◽

Convolutional Neural Network ◽

Network Model ◽

Neural Network Model ◽

Input Layer ◽

Fully Connected

Panthera merupakan genus dari keluarga kucing yang memiliki empat spesies popular yaitu, harimau, jaguar, macan tutul, singa. Singa memiliki warna keemasan dan tidak memilki motif, harimau memiliki motif loreng dengan garis-garis panjang, jaguar memiliki tubuh yang lebih besar dari pada macan tutul serta memiliki motif tutul yang lebih lebar, sedangkan macan tutul memiliki tubuh yang sedikit lebih ramping dari pada jaguar dan memiliki tutul yang tidak terlalu lebar. Pada penelitian ini dilakukan klasifikasi genus panther yaitu harimau, jaguar, macan tutul, dan singa menggunakan metode Convolutional Neural Network. Model Convolutional Neural Network yang digunakan memiliki 1 input layer, 5 convolution layer, dan 2 fully connected layer. Dataset yang digunakan berupa citra harimau, jaguar, macan tutul, dan singa. Data training terdiri dari 3840 citra, data validasi sebanyak 960 citra, dan data testing sebanyak 800 citra. Hasil akurasi dari pelatihan model untuk training yaitu 92,31% dan validasi yaitu 81,88%, pengujian model menggunakan dataset testing mendapatan hasil 68%. Hasil akurasi prediksi didapatkan dari nilai F1-Score pada pengujian didapatkan sebesar 78% untuk harimau, 70% untuk jaguar, 37% untuk macan tutul, 74% untuk singa. Macan tutul mendapatkan akurasi terendah dibandingkan 3 hewan lainnya tetapi lebih baik dibandingkan hasil penelitian sebelumnya.

Download Full-text