This book presents a new finite-difference scheme for hyperbolic conservation laws based on random choice. The authors show that this scheme outperforms conventional schemes in terms of accuracy and efficiency, making it a valuable tool for a wide range of applications. This book is an essential reference for anyone working in the field of numerical methods for partial differential equations. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.