# Approximate Solution of Riccati Differential Equation using He’s Variational iteration Method

• Vikramjeet Singh, Pankaj Kaushal, Monika Rani

### Abstract

Riccati equation is widely used in designing and analyzing linear and non-linear optimal control processes. In this paper, we have presented an analytical solution for the quadratic Riccati differential equation by He’s Variational Iteration Method. This method is relatively proficient and suitable for such problems as compared to classical methods. Firstly, a correctional function has been constructed with the help of a general Lagrange Multiplier based on variational theory and then the solution has been found for Riccati Equation without any unphysical restrictive assumptions. A comparison of the approximate solution with the exact solution has also been given. The absolute error of 3.28x10-6 to 8.74x10-8 has been obtained by the proposed solution. Our results show that the proposed method is very efficient and simple as compared to existing classical methods.

Published
2020-06-06
How to Cite
Vikramjeet Singh, Pankaj Kaushal, Monika Rani. (2020). Approximate Solution of Riccati Differential Equation using He’s Variational iteration Method . International Journal of Advanced Science and Technology, 29(4s), 3581-3584. Retrieved from http://sersc.org/journals/index.php/IJAST/article/view/24407
Section
Articles
{"ft_lang_label":"__label__en","ft_lang_prob":0.9458423,"math_prob":0.6479613,"size":978,"snap":"2023-14-2023-23","text_gpt3_token_len":188,"char_repetition_ratio":0.137577,"word_repetition_ratio":0.0,"special_character_ratio":0.17280163,"punctuation_ratio":0.06875,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95003766,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-06-01T06:46:19Z\",\"WARC-Record-ID\":\"<urn:uuid:ec3b43b0-0fbe-4606-97e1-68fd9eb5b281>\",\"Content-Length\":\"22832\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a111c5c4-80ea-407d-857a-57fe2b4878ba>\",\"WARC-Concurrent-To\":\"<urn:uuid:e863811d-4eaa-4675-bc70-bca093b3cce7>\",\"WARC-IP-Address\":\"184.168.99.77\",\"WARC-Target-URI\":\"http://sersc.org/journals/index.php/IJAST/article/view/24407\",\"WARC-Payload-Digest\":\"sha1:C27MZPGT3PTTAQV4WMMEDNROPA75O4YB\",\"WARC-Block-Digest\":\"sha1:375XHJQS2ZWY64RXJEMAOZ2AXNLX77VC\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224647614.56_warc_CC-MAIN-20230601042457-20230601072457-00034.warc.gz\"}"}