New Modification on Heun’s Method Based on Contraharmonic Mean for Solving Initial Value Problems with High Efficiency

In this paper, small modification on Improved Euler’s method (Heun’s method) is proposed to improve the efficiency so as to solve ordinary differential equations with initial condition by assuming the tangent slope as an average of the arithmetic mean and contra-harmonic mean. In order to validate the conclusion, the stability, consistency, and accuracy of the system were evaluated and numerical results were presented, and it was recognized that the proposed method is more stable, consistent, and accurate with high performance.

Perbandingan Algoritma Contraharmonic Mean Filter dan Arithmetic Mean Filter untuk Mereduksi Exponential Noise

Noise in the image caused a decrease in image quality, so that the image will look dirty and spots appear on the resulting image. Noise also results in reduced information on the resulting image so that noise limits valuable information when image analysis is performed. Filtering technique is one way to overcome noise. The filtering technique used in this study is using the Contraharmonic Mean Filter algorithm and the Arithmetic Mean Filter algorithm with the type of noise used to reduce the Exponential Noise. The results of the two algorithms show that the Arithmetic Mean Filter algorithm is a better algorithm to reduce the Exponential Noise compared to the Contraharmonic Mean Filter algorithm which is proven based on the value of MSE (Mean Square Error) and PSNR (Peak Signal-to-Noise Ratio).

Reduksi Noise Salt And Pepper Pada Citra Digital Menggunakan Metode Contraharmonic Mean Filter

Image is an object that is most often used for personal or public purposes, but the image is very susceptible to interference such as noise or noise where the image is exposed to noise or noise will experience black spots attached to the image. The existence of noise attached to the image needs to be reduced so that the image looks clearer using the contraharmonic mean filter method that can reduce noise in digital images. The image affected by noise after being reduced using the contraharmonic mean filter method, the image is much clearer after being reduced.

A double inequality for the combination of Toader mean and the arithmetic mean in terms of the contraharmonic mean

We find the greatest value ? and the least value ? such that the double inequality C(?a +(1-?)b, ?b + (1-?)a) < ?A(a,b) + (1-?)T(a, b)< C(?a + (1-?)b, ?b + (1-?)a) holds for all ? ? (0,1) and a, b > 0 with a ? b, where C(a,b), A(a,b), and T(a,b) denote respectively the contraharmonic, arithmetic, and Toader means of two positive numbers a and b.

Sharp Bounds for Neuman Means by Harmonic, Arithmetic, and Contraharmonic Means

We give several sharp bounds for the Neuman meansNAHandNHA(NCAandNAC) in terms of harmonic meanH(contraharmonic meanC) or the geometric convex combination of arithmetic meanAand harmonic meanH(contraharmonic meanCand arithmetic meanA) and present a new chain of inequalities for certain bivariate means.