Scientific Computing for differential equations involves application of mathematics for using computers to simulate and find accurate solutions to science and engineering model problems. The model problems are formulated mathematically with background in science and engineering and requires numerical methods and algorithms to be solved (approximately) on a computer with overall purpose of gaining improved insight at relatively low cost.
Research in this field involves both theoretical and practical aspects of developing, analyzing and applying different numerical methods and algorithms for the solution of both ordinary and partial differential equations. Important concerns are robustness, accuracy and efficiency of the algorithms and validation of the computed solutions.