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Pada umumnya orde dari persamaan diferensial adalah bilangan asli, namun orde pada persamaan diferensial dapat dibentuk menjadi orde pecahan yang disebut persamaan diferensial fraksional. Paper ini membahas persamaan diferensial fraksional Riccati dengan orde diantara nol dan satu, dan koefisien konstan. Metode numerik yang digunakan untuk mendapatkan solusi dari persamaan diferensial fraksional Riccati adalah Adomian Decomposition Method (ADM) dan Variational Iteration Method (VIM). Tujuan dari paper ini adalah untuk memperluas penerapan ADM dan VIM dalam menyelesaikan persamaan diferensial fraksional Riccati nonlinear dengan turunan Caputo. Perbandingan solusi yang diperoleh menunjukkan bahwa VIM adalah metode yang lebih sederhana untuk mencari solusi persamaan diferensial fraksional Riccati nonlinier dengan orde antara nol dan satu, kemudian hasil yang diperoleh disajikan dalam bentuk grafik. Kata kunci : diferensial, fraksional, riccati, adomian dekomposisi The solution of Riccati Fractional Differential Equation using Adomian Decomposition method Abstract. Generally, the order of differential equations is a natural numbers, but this order can be formed into fractional, called as fractional differential equations. In this paper, the Riccati fractional differential equations with order between zero and one, and constant coefficient is discussed. The numerical methods used to obtain solutions from Riccati fractional differential equations are the Adomian Decomposition Method (ADM) and Variational Iteration Method (VIM). The aim of this paper is to expand the application of ADM and VIM in solving nonlinear Riccati fractional differential equations with Caputo derivatives. The comparison of the obtained solutions shows that VIM is simpler method for finding solutions to Riccati nonlinear fractional differential equations with order between zero and one. The obtained results are presented graphically. Keywords : riccati, fractional, differential, adomian, decomposition

Differential equations are ubiquitous in many fields of study, yet not all equations, whether ordinary or partial, can be solved analytically. Traditional numerical methods such as time-stepping schemes have been devised to approximate these solutions. With the advent of modern deep learning, neural networks have become a viable alternative to traditional numerical methods. By reformulating the problem as an optimisation task, neural networks can be trained in a semi-supervised learning fashion to approximate nonlinear solutions. In this paper, neural solvers are implemented in TensorFlow for a variety of differential equations, namely: linear and nonlinear ordinary differential equations of the first and second order; Poisson’s equation, the heat equation, and the inviscid Burgers’ equation. Different methods, such as the naive and ansatz formulations, are contrasted, and their overall performance is analysed. Experimental data is also used to validate the neural solutions on test cases, specifically: the spring-mass system and Gauss’s law for electric fields. The errors of the neural solvers against exact solutions are investigated and found to surpass traditional schemes in certain cases. Although neural solvers will not replace the computational speed offered by traditional schemes in the near future, they remain a feasible, easy-to-implement substitute when all else fails.

This paper discussed about the construction of a model the relationship between a dependent variabel and a independent variabel using spline analysis regression. This methods is usually used when the relationship between variables is unknown. This methods is applied to construct the growth curve for children under 3 years of age in Padang.Kata Kunci: spline regression, growth curve, children under 3 years of age